How many more transactions per second will be possible with SegWit?
Best estimates on effective blocksize with SegWit are 1.6-2.0 MB.

Current transactions/second possible are around 3 tx/s. Given that the effective increase is 1.6 - 2.0x, the transactions/second are also the same multiple giving us somewhere around 5-6 tx/s.

The second question is harder to answer. There's a reason I wrote "effective blocksize" since segwit transaction sizes are different. However a straight blocksize increase on top of segwit indeed would be linear.