What those two bodies of government represent, and what is their respective responsibilities, in simple terms?

I'd also add to Q's response: the reasons the House and Senate each exist.

House representatives from each state are a percentage of the population. Senate representatives are two-per-state. The purpose of the House is to provide per-person representation, that is, true Democracy. The purpose of the Senate is to provide per-state representation, that is, to prevent states with huge populations from oppressing states with tiny populations.

Finally, is it "president" or "President" in English?

Proper American English requires capitalising the word 'President' in direct reference US past and current Presidents. For example, 'The President', 'President Obama', and 'former President Bill Clinton', but 'the president of the athletic club' and even 'the president of the United States'.

When not including the name, it gets a little tricky. 'President' should be capitalised when it replaces their name. So, 'The Civil War president freed the slaves', but 'The President is over there'.

Incidentally, 'Speaker' in reference to the Speaker of the House is the other exception to standard capitalisation rules. It is always capitalised. For example, 'Speaker Paul Ryan' and even 'Have you seen the Speaker?' The reason for this is probably to differentiate the Speaker of the House from someone who happens to be speaking. 'The Speaker recognized the speaker'.