What is the MAX charging current for a 3.7v 4000mAH Lithium ion battery cell

I'm building a little portable battery pack for some of my gadgets during those long plane flights. I have four 3.7v Lithium batteries (4000mah) I was going to rig in PARALLEL for a total of 16000mah of stored power.

I have two questions:
1) What is what's the highest charge current can these batteries handle?

2) Can I charge these batteries in parallel using a single charger that is designed to charge a 3.7v cell?

Thanks in advance!

[1] 4A . With this rate of charge,cell dies within one year.

[2] NO ! Unless you set up individual current control network for each battery path.