Can I charge Li-ion battery with current lower than 0.1 C ?

I order 18650 Keeppower 3400 mAh (Panasonic inside)
I have charger for smaller Li-ion batteries, but it has current 0.25 Amper only.
It will charge Keeppower for more than 10 hours.
Is it O.K. to charge with current lower than 0.1 C ?
(Charging Nimh batteries with 0.1 C is actually even better, my Sanyo AA last more than 10 years.)

My second question: My charger was cheap, but it is reliable, charged battery has always 4.15 V.
Is there any reason to buy expensive brand name charger ? Does it charge differently (beside the speed) ?

Yes, the expensive charger will charge faster and will charge correctly. It sounds like your charger may not be fully following the recommended charging method, so ML-102 (around 8 dollars) will be able to do that (and charge faster).

It is O.K.
The only difference is the termination point. If your charger really stops at 4,15V, this may be equivalent to a bigger charger set to 4.2V.

The ML-102 charger seems great.
Is this:

the same charger as this :


If you do not need USB-out, take ML-101