Technically, ALL SF ships would be exploratory type ships (oriented towards science).
The way they were designed seems to be 'ultimate versatility and exploration' in mind (at least before Ds9 decided to make 'dedicated warships') and probably an even match to most ships of neighboring interstellar powers the Federation is aware of.
No. Why would you think that? The Enterprise D is a capital ship, designed to be able to complete many different types of missions, including battleship. We saw quite a few of them in the Dominion War.
To my knowledge, it was never stated the Enterprise-D is a 'capital ship'. It may have been the 'flagship', but hardly what I would call a 'battleship'.
The closest we can come up with using canon data is that the Enterprise-D was a ship of exploration (and Voyager was also mentioned to be one).
What we saw during the Dominion War was a bunch of pre-existing Federation star-ships that were fighting against the Dominion - I don't think any 'military' designations were given to different Federation ships (except 'fans' who apparently had a need to transpose current day terms to something that was supposed to be inherently different - even Picard found it incredulous that a man from the late 20th century in 'The Neutral Zone' compared the Enterprise to a 'naval ship').
We also saw just 1 galaxy class featuring minor upgrades to its weapons systems... the USS Venture (which was modified with 2 extra phaser strips, each one on the top of the warp nacelles) - we hadn't seen other Galaxy class ships being outfitted with these phaser changes, and perhaps they weren't needed as most of the upgrades would probably occur on the inside to increase effectiveness against Dominion ships.