If I start a new game, will the achievements (guns and clues) go back to zero

At first, the credits available to you in the single player campaign is limited to that from missions alone. However, once you've fully maxed out either the zerg or protoss research trees, you gain the ability to trade any future research points into 10k worth of credits.

There have been mentions of a glitch with the way the game handles this: if you replay a mission you've already beaten and acquire protoss / zerg research points within that mission, it is possible to get the Moebius foundation to "purchase research samples" from you, even though you failed to increase your net points (you already got them once). In this way, you can accrue as many credits as you need, and can buy all the armory upgrades in a single playthrough.

Update: This method has since been patched.

As of now, the best way to earn the armory achievements is to play the campaign multiple times, selecting different upgrades on each playthrough, as achievements are shared across all campaigns.

Yes, you should have absolutely no issues doing that. I believe you should have most all of the Prestige related titles already, but I haven't gotten to 10 yet myself.

For more information on what you need to do to get the titles, the Call of Duty Wiki on Wikia has a full list of all Titles. The Prestige related Titles are listed with a green background.