As far as I am aware they didn't set out to make a trilogy. When TWOK was made, I don't think that had any plans to make a third movie.
Yes. If you notice the battle-damage on the effects miniature in III was far more extensive than that in II, as following TWOK ILM believed they would just be patching up and re-using the ship for the next movie. When Spock was slated for a return, and the decision made in the script for the destruction of the Enterprise extra battle-damage was added to make Stafleet's decision to decommission the ship rather than repair her more viable.
ILM were in fact hoping to use their new Excelsior miniature in the future, as they had not constructed the original refit Enterprise miniature and found it heavy and unwieldy to use (I read in an article somewhere that if one of the lights stopped working, they actually had to cut into the ship to replace it).
But certainly whatever the original intent TWOK-TVH does work as a great trilogy, and I regard it as such, more than once watching all three back-to-back.