What is the highest level of weapon mods that I can find, will I be able to find it without doing a new-game-plus?
The max level is 5 for mods, period.
You shouldn't have to play a new game plus to get them, though you will have to get to the end of the game for them all to unlock, they're not available from the start. You might have to play a new game plus to get the credits to afford all of them however, especially if you spend lots of credits on other items.
Actually, if one uses Gibbed one can get them to any level they wish (didn't try above 10 tho). On the downside, values won't show (will on the left graph for some, like accuracy, damage or capacity). Oh.. There is the possibility ME3 won't recognize such a savegame for new game+, or will reset the mods when starting one. Didn't try yet, too many chars to bother playing the same one again.