Yes, Lenka, you can. Can and could are often intercangeable; to name only one case: They say it was Hans who stole the money, but I don't believe it.
Hans can't have stolen the money.
= Hans couldn't have stolen the money.
Can I use "could" in the following sentence or should I replace it with "can"?
Please arrive early so that we can start the meeting on time.
My feeling is that it's grammatically possible but, maybe due to the imperative "arrive early", it's not semantically appropriate. What do you think, Philly, if the imperative were made more tentative, as in,
Could everyone please arrive early so that we ____, for once, start the meeting on time?
for tenses you can not use "can" instead of "could" and can not use "could" instead of "can"
When we make a choice between modals, Volcano, it's not a question of tense, because in modern English modals are tenseless. We make our choices according to the emotive/modal meaning we want to convey.
for ability you should use "can"
I agree that 'can' is the most likely/reasonable choice to describe one's abilities, Volcano, because generally, people are realistic about their abilities. But 'could' can also be used in some circumstances to describe ability.
"I could climb that tree, if I were so inclined/if I feel like it." = I have that ability if I chose to put it to the test.