Can I reconnect a normal chain with a quick link
You did not mention the type of your chain, but yes, quicklinks normally also work for other brands. SRAM quicklinks are known to work for Shimano chains etc.
Be aware that you must use 9-speed quicklinks for a 9-speed chain and similar. The widths differ so the the number of speeds must match.
You can solve some problems with wrong chain installation also by opening the derailleur cage (small screws), reinserting the chain, and closing agai. Under tension it could be tricky, though. Definitely take the chain off the crank first.