Learn English – What exactly the expression “make an argument” means

the purpose is that I want to work with you

This seems fine, though more context would be helpful. Some suggestions are

1. The reason is that I want to work with you.
2. (I applied to this position) because I want to work with you.

I think the your new device has a lot of possibilities to achieve more responsibilities of mine

I have some concerns.

1. Since you have one device, if it just has one function, but that function has many applications, then I would consider using "possibility".
2. Responsibilities can imply a sense of long-term tasks. In such a case, I don't think someone "achieves" their responsibility. It is might be better to use words that suggest that the devices helps with your responsibilities.
3. It is possible to end with of mine, but if you can squeeze the word my in the sentence instead, that might sound more natural.
4. There is also the matter of whether the device helps achieve the goal or does it without you. If the device can take care of your responsibilities without you, then you might use the phrase "relieve me".

Some possibilities are:

1. I think your new device has the possibility to help [me] with my responsibilities.
2. I think your new device has the potential to help [me] with my responsibilities.
3. I think your new device has the potential to relieve me of my responsibilities.

"It's certainly not a given" is a rather indirect way of saying that arguments exist against your position. If something is a given, it is not debatable and it is pretty much universally accepted.