I have about 6-8 connections. How many connections are necessary for effective connection to peers? The minimum?
Effective connection for what? The minimum you need is one connection.
If you connect to only one peer, if the peer has bad connection to the network, then will you have bad connections too?
Yes, by default though bitcoin core will establish 8 outbound connections. If your machine is unable to hold that many connections you should probably not run a full node. The chance that all 8 peer are badly connected to the rest of the network is very small as they each hold at least 8 connections as well.