First confirmation time vs miners fee's After submitting a transaction to the blockchain..

1) If I pay a higher transaction fee will first confirmation happen faster?

2) I found today that a 250B transaction with 1000 Satoshi fee took just under 2 hours is this normal?

3) Does the network I submit the transaction to make any difference to the fee and the time to first confirmation, as indicated here... http://p2sh.info/dashboard/db/fee-estimation

4) I hear that some miners prefer to mine transactions with no fee as it gives them some kind of advantage? Any information on this would be great
1) Yes. You can see some statistics here: http://bitcointicker.co/networkstats/

2) "Normal" will depend on network usage and how much others are paying. So can't give a definite answer there. Let's just say your fee should be competitive if you want your transaction included in reasonable time.

3) Shouldn't matter as all transactions are distributed around the entire network. Most of the miners should "see" your transaction very fast, so the time will depend on whether all the miners or just some of them decided to include your transaction in the block they're working on. Miners are free to have whatever policy they want on what transaction they want to include. Usually it's the highest fee that gets in. If the miner who included yours "wins" the block, your transaction will most likely stick on the blockchain, and after a few more confirmations, definetely.

4) Not exactly sure on this one, but it doesn't make much sense to me. I know miners sometimes decide to mine an empty block. Not sure what is the benefit though, could have something to do with network propagation. Maybe someone else could shine some light on this.