Duplicating a KeeLoq Remote Control
Q1: since KeeLoq defines the crypto used: yes, if you use an insecure crypto method, then no matter how you implement it, it will stay insecure

Q2: doesn't apply.

Note that KeeLoq has a stronger variant with a secret internal seed that will be much harder to clone (it's possible, I think it's been shown that with all existing implementations you can apply power usage side channel attacks that work well). 

Also note that you must not believe what is said about products on ebay. they lie. Remotely copying KeeLoq isn't that easy. You can certainly, by timing-specific jamming, grab two codes, and only forward the first one to make it seem like the system works normally, storing the second one for later unlocking, but that doesn't "copy" the remote, but only a single unlocking code. Still, it's a weak system; it can be replicated by observing a very limited amount of codes. (The improved system remedies that by including 60bit of entropy, which explodes the number of required observations). The rolling code remote replicators might apply to other, common, rolling codes (for example).

The wikipedia page has more info.