Just tell me this: If miners get less reward, does the transaction fees decrease?
No. Miners are free to charge you whatever they wish. Since they get only 1/2 the coins (12.5 BTC) for solving a block, they may wish to make up for that in fees. Or not.
Also, with less miners, will transaction time elongate or with half the total bitcoins, will the transaction time decrease? Along with halving, are cold wallets with no balance about to be removed?
When miners go offline, hashrate goes down, blocks will take longer to solve, and transactions take longer to confirm. This will be compensated for at the next difficulty adjustment, which will happen after 2016 blocks are solved.
https://en.bitcoin.it/wiki/DifficultyIf you want the boring stuff, some more details:
1. Miners don't have to include your transaction, so if you didn't include a high enough tx fee, or they simply don't feel like it, your tx won't be included in the next solved block.
2. Difficulty is not adjusted continuously, but only once every 2016 blocks. If enough miners go offline at once, the difficulty doesn't immediately go down. see my previous post.