What is the best way to raise the alliance combat rank, technology ... individual cp, number of members..

If you mean the alliance power rank, the total alliance power is the sum of all the members total power values. So to increase it you need more members and members with high power.

To increase the power the members need to upgrade, research and train troops. The best way to help is to keep them protected from attacks and help them with gaining resources etc. this is not easy but perhaps setting up farms that they can raid will help.

Encouraging peace in your state can help with completing clash of zones events which will bring big rewards.