There's no way to tell because everyone heals differently. 2 months is still pretty new so I wouldn't risk leaving it naked. If you have to take it out for work or something, put a clear glass retainer in it.
stitches...
Pain and discomfort are part and parcel of getting the cartilage pierced with a piercing gun. The piercing gun user knows that they are not allowed to pierce ear cartilage with a piercing gun. Properly done cartilage piercing done by a professional body piercer would have been healed by now. The swelling is due to the stud backing being too close to the skin and not allowing the piercing to drain or breath properly.
There will be bumps in the cartilage near the piercing. It is better to be pierced with a needle.
How long has it been pierced
Your question isn't very clear, but I will give it a shot. The time it takes for a navel piercing to close or "heal up" depends on how long you have had the piercing. The longer the piercing has been in place with jewellery, the longer it will take for the piercing to close with the jewellery removed. Generally if you have had the piercing with jewellery over a year the piercing can take several months to shrink down to the point where you can't put jewellery into the piercing any longer. If you have only had the piercing for a few months then it can take a few weeks for the piercing to close.
Depends on how long you've been pierced...for a new piercing i would limit it to no more than 15 mins for the first month or so...if you've had the piercing for a few months i dont see why you couldnt...
It depends on how fast your body heals and how new the piercing is. But even piercing that have been done for years can close in minutes. So there really isn't a way to tell how long it takes. So I would try to put jewelry in asap if you want them pierced.
Some people's bodies are different when it comes to the healing process. Take out your piercing and just wait. It may take from a couple months to a year to close. Everyone's body is different.
If it's recently been pierced, then yes. Any piercing is likely to swell.
How long a piercing takes to close up depends on the gauge of the piercing but mostly it depends on the individual. All I can give you is anecdotal evidence; I removed my 14g lip piercing which was 18 months old and was unable to re-open the hole without re-piercing just two days later. If you want to keep the piercing open but need it to go unnoticed (say, for a job interview or a particular event) consider using a piercing retainer, these are clear plastic bars which are almost invisible when worn.
No, you can't. And you should never get anything pierced with a gun; they're dirty and never cleaned properly. Would you want to be pierced with something that's pierced someone else, and not even been cleaned?
Like any hole in the body that wasn't there by design the piercing will close if jewellery is not kept in the piercing. The speed at which the piercing closes will be dictated by the period of time the jewellery has been kept in the piercing, the longer jewellery is worn the longer it will take for the piercing to close up.