Yes he does benefit from entrenchment bonuses and healing while in your city with a ROW. If you want to make sure just hover over the castle icon in the top right of the unit information. Once he declares war, however, he forfeits those bonuses.

Well I have one:
If I enter enemy city without troops but there are foreign troops inside from a country I am not in war, will we automatically start a war?
And what will happen in the city at that moment?

Asking because had situation like this. Took the city but instantly went to war with foreign country. And we were both attackers even I took the city first. I did not have a defensive bonus, I was attacking too. Maybe because I used jumping trick or this is usual that both sides are in attacking mode?

The only thing I'm sure about in that statement is that running into another player's troops without ROW or a coalition will start a war. A simple peace request after the fact should solve this.

No no it was not a problem, it was my intention. I was ready and destroyed large force guarded several empty foreign cities. Well the cities of my first enemy. But I knew next is the "guardian". They weren't in a coalition btw. Just RoW. The "guardian" told him to attack me with all his troops and he will defend him. First guy lost all the troops and didn't even manage to reach any of my cities.
Than I decided to enter the his cities and deal with the "guardian"

So I destroyed probably 300+hp of troops because I had everything there. Arty, helichopters, airplanes, ground troops.. And I did it very quickly without losing troops. Maybe I lost 1 single recon vehicle that was already half hp. It was.. so good..

The only thing I didn't figure out was that ground troops attacked each other. No defender when the battle started even city was mine instantly. Technically I was a defender because it became my city before war started. But we both attacked each other in that battle.

Foreign troops ignore you, until you conquer the territory and your troops will attack them, to 'defend their territory'.

Every troop get the center of province benefits, as long it is not considered 'attacking'.