Does it matter if id (in TABLE ) starts from 0 or from 10000 Sorry for my incorrect terminology (as I don't know what to call that)..
does it matter (with regard to performance) if unique (index) key starts from 0 and from i.e. 100000 ?

For example, if I have

ID     |  Brand
----------------
1      | BMW
2      | FERARRI


or 

ID     |  Brand
----------------
100000 | BMW
100001 | FERARRI


will be there any difference for performance/queries? I ask that because I have a PHP function that deletes everything and inserts new values. Thus, delete/insert/delete/insert causes to increase the ID more and more, and I am afraid, if I will eventually meet a problem? Or that's not a problem?
Your database shouldn't care, and to it a number is a number is a number in this context. Performance will be the same either way here.

Just make sure that you select an appropriate data type so that you have enough room to "grow" and don't hit the upper bounds of that data type in your expected usage (e.g. don't use a smallint if you're going to need your IDs to go out to 2 billion).