1. Which do you think is the problem?
Any of the two may be the problem. A defective remote or main unit. The main unit may be covered "too much" preventing recetion of signal from remote or wrong installation.

2. Is there away to activate manually the car alarm main unit?
This feature depends on the model and unit if the unit has this feature.

3. Pwede bang ipagawa ang remote key, or disposable lang ito?
There are some brands which have very good aftersales service that they can repair even the remote. For some ay patapon na ito. Try asking your vendor if they can repair the unitor sell replacement parts.