What can be considered to be general parameter for a coin to be established and safer relatively to be invested upon?
A safe parameter would be to consider the coins with larger market cap, such as BITCOIN, RIPPLE and ETHEREUM. Those coins are less volatile than others and they are *probably* not going to zero anytime soon. They have a high active dev team and are somehow trusted.
Their marketcap is very high, billions of dollares, so they are somehow safer to invest.
That the coin is stable?
No coin is stable. Only Tether and other stable coins, which are pegged to USD value. 1 Tether = 1 USD always.
Consider CoinMarketCap, where does it mean that if the coin is listed here it is established? OR if it is in the top 1000 or if it is in the top 500 or 100?
Listing in CoinmarketCap(CMC) only means that the coin is listed in a exchange that CMC recognizes.
In general, top3 cryptocurrencies are the safest. In the Top100 coins you will find many possible scams (like bitconnect).
Apart from CoinMarketCap are there ways to evaluate or estimate the stability and establishment of a coin? Or do we find such coins in certain exchanges such that the exchange is very particularly choosy or that it has a certain clear performance index as a measure for a coin to feature therein?
The best way to evaluate the coin you are interested is a fundamental analysis, which cannot be done in CMC. You need to read the whitepaper, look information about the team, see if they are legit, and if their business is needed. If the coin has any reason to have any value.... Even if they are all ok, their business may not be lucrative. It´s a high risk/reward.