1) This is the first time in history that an official presidential portrait was taken with a digital camera. - This should be "has been taken with a digital camera". However, an NES could say "was taken with a digital camera".
2) This is the first time she shared it publicly. - This should also be the present perfect, "she has shared it publicly". Or it could be "That was the first time she shared it publicly". The speaker probably really meant "This is the first time ...". And, once again, an NES could say something like this. It's possible.
3) This is the first time you're working a game for her/his team. - This should be "you've worked a game for her/his team". If the action is in progress at the time of speaking, I can imagine an NES saying this. It wouldn't be so bad, but, of course, it would not conform to how your ESL grammar books told you to say it.
4) ...that in 20 years of going to this church, this is the first time he realized that these kind of things were going on... This could really just as well be present perfect. I would say it should be, but, again, NESs say things like this from time to time. It should be "the first time he has realized" for this sentence. You could say "that was the first time he realized ...", but then we move to the past. I think this speaker meant this to be in the present.
5) This is the first time that I've heard her sing. - There's no problem with this one.
So, here's what I would advise. Even though you'll hear native speakers use these types of sentences (structures? whatever), I would advise you to simply write and speak as you've studied. There's less confusion in this way. I wouldn't be concerned at all about adapting these sorts of deviations in verb form usage to the way you use English. You could hear NESs talk this way from time to time, but that's about it. I wouldn't try to mimic native speaker speech right down to the frequency with which some people might use some of the types of sentences you posted here. It's not worth the hassle. Take note, observe, and listen. That's what I would do.