To start Bitcoin mining, you will need a Bitcoin wallet,a ledger is the best choice, mining software, and mining hardware,asics are expensive. you will need to download and install mining software on your computer. Once you have the software, you can start mining by using your computer's processing power to solve complex mathematical problems that validate Bitcoin transactions and earn new Bitcoin. You will also need to build or purchase a mining rig(asics), which is a computer specifically designed for mining cryptocurrencies. It's important to note that Bitcoin mining can be a competitive business, but the equipment can be a lot expensive
Yes but no. There is no software to install on your computer, you just need one or more ASICs, and you need a internet source. You can then access the interface of your server via its IP address but no specific software is necessary.
You have to stop saying all the time that mining is "complex mathematical problems solving", it's totally wrong. It is closer to bruteforcing than to solving a complex mathematical problem. This is a preconceived idea that is totally wrong.
Otherwise, to answer OP, the only intelligent way to consider mining is to know your electrical cost per kw/h, to understand the basic notions (difficulty, luck, types of payments according to the pools etc...), and to know where and from whom to buy your equipment so as not to get ripped off.
The only advice I can give you is not to be impulsive and to inform yourself a lot before spending money, because a bad choice could cost you a lot of money.