"Why can I not use present tense?" You could use present tense, but it will feel awkward (as you yourself noted). I think it should seem odd.
Photographs are interesting objects. When you hold a photograph, you are actually holding a piece of the past. The objects in the photograph are from the past, and it makes sense that the past tenses would feel most natural. In the same way, when you tell a story about an event from your own life, you use past tense because you are describing events that began and ended before now.
If you decide to use the past perfect, you should make sure that you are using it to indicate that one event preceded the other. You could use it here, but it might not be necessary. "Her friends had asked her to smoke, but she hesitated. (You could use "seem," but you could also use a variety of verbs that show indecision rather than tell her indecision).
You could also use past progressive, but make sure that you are applying that correctly. Ideally, you want to use that for actions that interrupt other actions. For example, "Her friends were offering cigarettes to her when she looked away." I don't think this is quite as smooth, but maybe you have other ideas.
When speaking about a photo, or anything, you may use more than one tense. This can get tricky, but here is a little guideline: If you are describing the past, use a form of the past tense. If you are commenting on it now, present tense is fine. Note that only one of your examples uses two tenses. "My mom danced a lot. Didn't she seem to have a good time?" Remember than when writing questions, the verb that carries the tense is the one that is moved to the front of the sentence (in this case a form of to do. An example using a question that uses past and present might be, "Mom danced all night. Do you think she likes to dance?" In this example, I am using the present tense to indicate a state of being that is usually true "liking to dance." This is a standard use of simple present tense.
You may be noticing that simple present is not really that simple. It shows up often in text-books because it is the tense for giving instructions, "Read these sentences and write some other sentences." Other times, it establishes a normal state of being, "Freddie goes out to walk on Monday mornings." The most common use for simple past involves verbs like "to be" and "to have" in which the author is declaring a state of being that may or may not last for a long time, "The world is a vampire" (Smashing Pumpkins) or "I have all of the marbles!"