I think you wrote that you got your car at a dealers. They should have a warranty with it, so I'd take the car back to them and let them do the work and repairs. Even if it isn't a Volvo dealer & shop, they should stand behind their warranty. If it is a Volvo dealer, so much the better. if they can't fix it, don't accept that. I have a 2013 C70 which I bought from a Mercedes dealership. I spotted the roof liner not working correctly, and they had to send it to a Volvo Shop to have a new one installed (on their nickel). And, when a Volvo Shop repairs anything, they stand beside it for the life of the car (your ownership) - even the parts. That's why I take my C70 to the Dealer's. Sure, I may pay a bit more, but the guarantee is worth it, and I also get a free loaner until the C70's fixed. ( I do work on changing the oil, filters, plugs and the like. I like getting my hands a bit into the car.)
Don't get too "deep" into fixing the problems; that may void the warranty. Let them do that work for you.
By the way, do NOT work on the top yourself! Lubing is fine and maybe making sure that the cables (inspect those carefully! If they are frayed, start looking for them right now. Some are almost impossible to find!) and wiring is hooked into their holders. That's important: a crushed cable will be a real headache, and not a cheap one either. Find a shop that has an experienced, certified top mechanic. Ask specifically for that.
I also discovered that using the OEM spark plugs worked wonders. I had "as-good-as" plugs in it, but when I went to the Volvo ones, it's like the car woke up.
If you want to do something good for the handling, (and, it's almost a necessity) buy an over-the-engine' stabilizer bar. That, with a beefier rear one, will almost eliminate body roll, which this car is notorious for. A windscreen is a good idea, too. They help disperse the wind when your driving with the top down, so you can easily hear the other person, and, you don't feel like the wind beat you up on lionger drives.
I had an '06, and loved it so much, had to get another C70. They are a fun car, and in my opinion, Volvo's best.
Have fun with it!
Drive laughing!
Tedders