transaction broadcasts, declining node count, mining basics and costs.
When making a transaction, it is always broadcast on the entire p2p network. Either from the node your wallet is running on, or from the connected node, in case of a light wallet (SPV).
Value is not connected to node count. Security only to a minimal degree. The decrease must  be a short term effect. In the long run, node count will increase with adoption.
In theory yes. In reality, you would point your miners to a pool, which will be running a node.
Unless you have to access to electricity at industrial rates, mining is not profitable any more. The profits you might make will be from BTC price appreciation, which you can also achieve by just buying and holding BTC.
You can calculate your rewards by the ratio of your equipmemts hashrate to the overall network hashrate. E.g. you have 1/100000 of the network's hashrate under your control, you can expect to mine 1/100000 of the block rewards, which will yield you 0.000125 BTC every 10 minutes.
Avoid cloud mining, as it is more profitable for the service provider than you. Often, those operations are even outright scams.