transaction broadcasts, declining node count, mining basics and costs. I read a lot about bitcoins and mining and nodes but there are a few questions that are still not answered, which are the following:


As I read when a transaction is broadcasted, at first it gets confirmed by active nodes and later goes to mempool and miners pick the ones with higher fees. So the question is, when I make a transaction on a website how can I make sure that the website is broadcasting my transaction? Maybe the site is holding it because it has high fee so that he can include it in his own block?
I noticed that nodes are becoming fewer every day , does this mean
when they become less the security of bitcoin or its value will
decrease ?
In order to become a miner, do you have to be a node too? 
Btc.com has a crazy fast hash rate. Is it even worth to get into mining? 
Say I want to become a miner with a chance of solving at least one block in a month, approximately how much should I invest? And should I buy cloud space or mine on my own?
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.