For the first part (12:30 PM standard = ? New)
See the explanation below for the relationship between "seconds" and standard seconds. 12:30 PM standard clock is 45,000 out of 86,400 standard seconds through the day. This is a ratio of 0.5208'3 of a day. Multiply this by the 200,000 "seconds" of a day, and we find that we are 104,166.'6 "seconds" into the day; we can convert this to the clock reading by inserting colons: 10:41:66.'6, or 10:41:66.'6 PM (rounded to the nearest "second", 10:41:67)
For the second part (5:75:75 PM = ? standard)
Your modified clock contains 200,000 "seconds" in a 24-standard-hour day. PM in a printed time indicates that it’s in the second ten-"hour" period, so to convert it to non-AM/PM time, just stick a 1 in front. We can then just delete the colons (because they represent divisions at 100), meaning that the time is 157,575/200,000 of the way through the day. The relationship between "seconds" and standard seconds is 86,400 standard seconds = 200,000 "seconds". We thus multiply 157,575 by 86,400, then divide by 200,000, to get the number of standard seconds into the day we are: 68,072.4. Two successive divisions by 60 (to convert from seconds to minutes, then from minutes to hours) gives us 18.909 hours out of 24. Taking the fractional part (0.909) and multiplying back by 60 to get minutes yields 54.54, and taking the fractional part of that (0.54) and multiplying by 60 to get seconds yields 32.4. Thus, the time as shown on a normal clock would be 18:54:32.4, or 6:54:32 PM (rounded to the nearest "second").