Question: does this mean that you also lose any future use of the symbol on it ?
Answer: Yes. When the card is removed from your deck there would be no way for you to use those icons in the future.
Question: are they the only cards to be used (for their action) in Combat, or can other non-"Combat" cards be used as well for their action ?
Other non-combat cards can be used but only if they directly add to your military strength.
Question: does this apply also to "reserve" cards put in the left slot (i.e. potentially granting 4 permanent effects, or even 6 with +1 reserve counter) ?
Yes, reserve cards give their reserve effect regardless of which reserve they are placed in. The only limitation is that Reserve Two can only hold reserve cards.
Question: do non-“reserve” cards also have permanent effects if placed in the reserve left slot?
No. Reserve cards are the only cards with an ongoing permanent effect. Non-reserve cards in your reserve just wait until you use them as if in your hand.