Do I need to add ampicillin in starter culture if miniprep or do I need to add kanamycin also because my plasmid (pQ30) contains ampicillin resistance gene and M15 pREP4 contains kanamycin-resistant genes
To be safe and avoid the loss of both plasmids, you should add both selecting antibiotics. Also, if available, you should prefer to use ticarcillin or carbenicillin, which are less readily destroyed by beta-lactamase than ampicillin.
Yes you will have both plasmids in your mini prep. But when you do your transformation you can just select for the plasmid you want (I presume Amp in this case). And then test your colonies to confirm whether they are also kanamycin resistance or not. You will get some colonies with both plasmids and some colonies with just the one.