No, the number of full nodes is decoupled from capacity and fees.
Transaction capacity is a function of transaction size and blocksize. Blocks occur roughly every 10 minutes and have a fixed size. Transactions also have a more or less fixed size, so capacity is currently not going to change unless either transactions get smaller (e.g. Schnorr signatures, MAST) or blocks get bigger (e.g. SegWit, blocksize increase).
Fees are a function of supply and demand of blockspace. Since the number of transactions that can be confirmed is limited over time, transactions with higher fee per byte get preferred. Especially when the network is unlucky and blocks are slow for a period the transactions waiting to be confirmed may build up intermittenly, which makes the average fees in blocks peak.
Full nodes are still important: Besides allowing their owner to trustlessly use Bitcoin, they serve as information providers to thin clients. If their number would be much smaller, the full nodes would be overwhelmed by these requests.
"More nodes does equal more mining power,[…]" I don't think that this is still true. Most nodes don't indicate mining operations anymore, and mining at home no longer makes sense. – Murch – 2017-01-07T23:23:30.023
Sorry, I interpreted "It seems to me having more Nodes verifying transactions" this as being OP only talking about nodes with mining power attached and not nodes without. All nodes do actually mine, nodes with just a PC attached don't do it very quickly, but they all do mine. Usually the thing that miners search for becomes public to the network before a normal PC/server can find it. – jackg – 2017-01-07T23:31:35.823
1No, that's not true. Mining was disabled by default in Bitcoin-Qt (now Bitcoin Core) years ago. I think in 2012 or 2013. Nodes don't mine unless you explicitly turn it on (and that would be a waste of power). – Murch – 2017-01-07T23:38:36.850
They still have to validate blocks using a given has and the specific block. That could be conidered a way of mining. Although nodes won't actually mine the coins themselves (in the way that ASICs and toehr hardware will). – jackg – 2017-01-08T00:01:37.573
Well, not really. Mining is the creation of new blocks. But they do indeed retrace some of the calculations done in mining. – Murch – 2017-01-08T00:03:26.127
1Every PC in the world combined wouldn't make a dent in the amount of hashing done per second right now. "More nodes does equal more mining power" is blatantly false. – Pieter Wuille – 2017-01-08T13:43:25.920