Yes, You can use Sony MBH20 with Nokia 3310.
Sony MBH20 comes with Sony battery only. As per company, it offers up to 100 hours of standby time and about 7 hours of talk time.
Yes, Sony MBH20 does have call ending button also.
Yes, You shall receive USB Cable for the same as part of the standard packaging.
None of the users have reported any heating problem about Sony MBH20.