Some questions about the tavern scene in Inglorious Basterds

Hammersmark is a public figure with international connections (more so than the average person). Given the nazi propaganda machine and things like the gestapo; it's more than likely that she is being watched.

If three strangers had shown up at her house, gone in, and left an hour later, that'd be highly suspicious to anyone watching her for unexplained affiliations. Even if not enough to conclude she is definitely compromised (from a nazi perspective), it raises enough suspicion to keep her out of the loop, so as to not risk her being compromised. That directly impacts her ability to spy on nazi intelligence.

So where would a person reasonably talk to strangers without raising any particular suspicion? A public tavern. it's the most common place where you'd exchange words with strangers, possible for an extended time, even if you never met them before or after.

Couldn't they have managed with an English photographer

She'd still be seen affiliating with an Englishman, which raises similar suspicions.

and two German photographers or something related to the film industry?
Also, why did the three Basterds meeting with her have to impersonate army captains?

The three Basterds are soldiers. Soldiers are often recognizable. Not only the haircut, but general posture and behavior often becomes visible.

Unless they were trained for infiltration, which the Basterds were not - they often lack that exact kind of finesse. The "Brad Pitt as an Italian" scene proves as much.

By having them pose as nazi soldiers, it's not suspicios for them to look and behave like soldiers. It's a great disguise (compared to any other German disguise) because of it.

On top of that, not many people would openly engage or question nazi soldiers, which lowers the chance of them slipping up when interacting with others.

I won't focus on the first question since it has already been answered.

Why impersonate Nazi officers?

In a Nazi-dominated France Nazi officers would have less trouble getting in and out of places without raising suspicions, having to show papers, and they would be considered a higher authority than any civilians of any nationality. This way the only ones that could defy their word or bother them would be real Nazi officers.