I'm not entirely sure that it is possible if the target is allowed to act completely arbitrarily, and you cannot make any additional assumptions about the behaviour of the no-man.
Due to the nature of the other two people, questions you ask will never actually give you any direct information about other people. The yes-man will answer yes regardless of whatever you say, while the no-man(because almost-always-no-man is too long...) will answer no except for any question of the form "Does X love dogs?", and even then the actual identity of X is irrelevant. Given this, the target could randomly pick one of these two, and answer questions exactly as if he were them. I'm not sure if this is what the question means when it says "He answers according to his outlook."
I'll take a crack at it anyway, and see what the minimal assumptions might be to solve it. I'll use some basic information theory to explain my approach. Let's call the 3 people A, B and C.
Now, at the start, there are six possible configurations of A, B, and C(Y = yes-man, N = no-man, T = target): YNT, YTN, TYN, TNY, NYT, NTY. Assuming they are all equally likely, this would mean that the entire "system" has an entropy of $log_2$(6) ~ 2.6 bits. You can only get 2 bits of info at most by asking 2 questions, so clearly finding the exact configuration is impossible.
Information theoretically, the location of T should be given by an entropy of $log_3$(3) ~ 1.58 < 2 bits, so the right approach would be to isolate T from the others. This requires a way to generate a question that T would answer differently from Y and N, which is impossible without somehow banning the "arbitrary answers" strategy. So, given all this, under the assumption that "based on his outlook" represents a greedy strategy from T(where without indulging in meta-think he just tries to directly answer questions as if somebody else is T/he is not T)...
Ask A: "If I asked B if he likes dogs, what would he say?". If the answer is yes, A is either N(since he was asked about liking dogs) or Y(he always answers yes). If the answer is no, A is T(since from a greedy POV, making B look like he is not N seemingly reduces an outsider's view of the probability of A being T from 1/3 to 1/4).
If question 2 is needed,
Ask B: "If I asked C if he likes dogs, what would he say?". By a similar line of reasoning, if the answer is yes, B is Y/N, and C is T, else B is T.
This is the first time I'm actually trying to solve a puzzle here, so any pointers/corrections would be welcome!