Around the world to a mystery country

Question

What country does this picture represent? Please explain your reasoning.

Some exhibits follow to help you out. Exhibits 1, 2, and 3 will get you started. Exhibit 4 will point your way.
Disregard the rivers, no special meaning.

Hint:

Exhibits 1, 2, and 3 demonstrate equivalency

Hint 2:

Top of a morning (2)

Hint 3:

Don't fear the knowledge tag; the mechanism is quite simple. Consistency in mapping pictures to text is key.

Hint 4:

Look left of gazelles (4)

Exhibits

1a

1b

2a

2b

2c

2d

3a

4a

4b

4c

4d

4e

4f

4g

4h

4i

4j

4k

4l

Answer 1

To follow on from @Randal'Thor's findings and our discussions in comments, I believe I have now sussed that the mystery country the OP is seeking is:

SPAIN

To find this, firstly note that Exhibits 1, 2 and 3 are supposed to be 'equivalent' (as per Hint 1). We have already sussed that we are supposed to extract specific letters from the name of the countries and cities depicted in each map, but so far we have been a little slapdash in which ones we select in each instance. However, there is a hard-and-fast rule set as to how to extract these letters, depending on the map sections shown.

The rule set is:

1. If a city is shown as a red dot, the name of the city takes precedence over the name of the country; else, use the usual shortform name of the country.

2. If the top/bottom half of a country is shown, take only the first/last letter of the name, respectively. [Hint 2]

3. If the left/right half of a country is shown, take the left/right half of the name, respectively. [Hint 4] If the name has an odd number of letters, include the middle letter.

4. If the map has been flipped, simply swap 'top' for 'bottom' or 'left' for 'right' (or vice versa).

To test these rules, see the equivalence of Exhibits 1-3:

Exhibit 1:
1a CANADA (left half) = CAN
1b BRAZIL (top) = B

Exhibit 2:
2a CUBA (top) = C
2b ANKARA (top) = A
2c PAKISTAN (bottom) = N
2d BRAZIL (bottom, flipped = top) = B

Exhibit 3:
3a CANBERRA (right, flipped = left) = CANB

i.e. In all 3 instances, the maps represent the 4-letters string CANB

Now that we have proven our rule set, let's extract the required letters from Exhibit 4:

4a MALI (left) = MA
4b GREECE (top) = G
4c GREECE (bottom) = E
4d LISBON (bottom, flipped = top) = L
4e MILAN (left, flipped = right) = LAN
4f ALGIERS (top, flipped = bottom) = S
4g FRANCE (top) = F
4h LAGOS (left) = LAG
4i HONDURAS (bottom) = S
4j HONDURAS (top) = H
4k ICELAND (top) = I
4l PERTH (bottom, flipped = top) = P

All together, this spells out MAGELLAN'S FLAGSHIP.

This is the helpful clue we need to help us identify the country depicted in the simplified map of the main question (since the map alone makes this a very difficult challenge), which is:

TRINIDAD AND TOBAGO, since the flagship of Ferdinand Magellan during his circumnavigation of the world was the Trinidad.

Next, identify the red dot in the image. This is the country's capital city:

PORT OF SPAIN.

Finally, note that the map shows the left-half of the country, flipped, meaning we need to take the right half of this. If we apply the rules we have already established, this should give us:

FSPAIN (including the middle letter). However, here I surmise that there is one more rule to include in our rule set - that if the city has a minus sign beside its dot, we are supposed to exclude the middle letter.

With this addition to the rules, we can now see that our final answer is SPAIN!

One final remark - this is an appropriate choice of final destination given the puzzle's context, since:

Magellan's voyage around the world (as per the title) actually began and ended in Spain!

Answer 2

Identifying the countries

An important realisation, along with recognising maps, is that

not all of them are full countries (some of them are just parts of countries), and some of them are rotated or reflected to be not in their usual orientation.

Exhibit 1 - two parts

1a is CANADA (western part).
1b is BRAZIL (northern part).

Exhibit 2 - four parts

2a is CUBA (western part).
2b is TURKEY (northern part) with ANKARA in red.
2c is PAKISTAN (southern part).
2d is BRAZIL (southern part, flipped top to bottom).

Exhibit 3 - one part

3a is AUSTRALIA (eastern part, flipped right to left) with CANBERRA in red.

Exhibit 4 - twelve parts

4a is MALI (western part).
4b is GREECE (northern part).
4c is GREECE (southern part).
4d is PORTUGAL (southern part, flipped top to bottom) with LISBON in red.
4e is ITALY (western part, flipped right to left) with MILAN in red.
4f is ALGERIA (northern part, flipped top to bottom) with ALGIERS in red.
4g is FRANCE (northern part).
4h is NIGERIA (western part) with LAGOS in red.
4i is HONDURAS (southern part).
4j is HONDURAS (northern part).
4k is ICELAND (northern part).
4l is AUSTRALIA (southern part, flipped top to bottom) with PERTH in red.

Next steps

(thanks to @Stiv for some help here!)

The OP says that "Exhibits 1, 2, and 3 demonstrate equivalency", so maybe we're meant to get:

1. CAN from Canada, BRA from Brazil;

2. C from CUBA, A from Ankara, N from Pakistan, BRA from Brazil (again);

3. CANBERRA from Canberra.

Then the meaning of Exhibit 4 might be along the lines of:

MA from MALI.
G or GR or GRE from GREECE.
E or CE or ECE from GREECE.
N or ON or BON from LISBON.
M or MI or MIL from MILAN.
A or AL or ALG from ALGIERS.
F from FRANCE.
LAG from LAGOS.
S from HONDURAS.
H from HONDURAS.
I from ICELAND.
P from PERTH.

It looks like we're getting

something FLAGSHIP, but I can't figure out the early parts. Maybe the red + next to Milan and Lagos in the maps indicates that we should take more than half of those words, so it's MIL and LAG. From the early parts it looks something like MAGHREB but not quite.

I suppose the answer might be

ALGIERS, if that city can be seen as the flagship of the Maghreb. But probably not.

Some older guesses

Maybe each country is represented by a code, such as its two-letter internet domain or its telephone prefix. Then

taking just half of a country could mean taking just one letter or number from such a code. But that wouldn't explain the significance of flipping some of the half-countries,

so it's probably something else. Maybe codes aren't involved at all and there is some pattern in the given countries which points towards whatever the final one is to be identified. Another option could be

1. CAN/BRA
2. CU/TUR/STAN/LIZ
3. AILA(R)
4. MA/GRE/ECE/LAGU/(A)TI/(E)GLA/FRA/NIG(E)/URAS/HOND/ICE(L)/AILA(R)

The interesting thing here is that

CANBRA is almost CANBERRA,

but it might be a coincidence as I can't make much sense of the rest.

The red dots also need to be taken into account:

some but not all of them are capital cities, some of them have a red + or - next to the dot but some don't.

The cities featured are

Ankara; Canberra; Lisbon, Milan, Algiers, Lagos. I couldn't spot any pattern in these yet.

Answer 3

Solving some of the clues first

1a

Canada

1b

Brazil

2a (uncertain)

Finland

2b

Russia (does the red point matter)

2c and 2d (?)

3a

SW Australia

4a

Looks like some US/Canada border between states/provinces

4b

Greece

4c

Should be Indonesia

4e

Some city in Italy

4g

Northern part of France, perhaps a province's name?

Next step:

Looks like the next step is to take one letter from 4a-l, giving a 12 letter answer. Not sure how to use Clues 1-3.