You don't normally "try a skirt out", which would imply you want to see how it performs (Does it light up? Change colours?). You "try a skirt on" - that is, you see if it fits and looks good on you.
Yes, I've reported it.
'Can I try on this skirt?' is surely the same as 'I can try on this skirt?' ?
I have a question that is not strictly related to this exercise. Let's say I am in a boutique in Paris and I am looking around, having a look at the garments displayed and suddenly I see something that catches my eye and I want to try it on. At this point, is it more common to ask: "est-ce que je peux essayer ce manteau?" or "peux je essayer ce manteau". Which sentence is more polite? or maybe there are other ways, which are even more common, to ask the same thing?
Can't help you with the main part of your question, but I do know that one does not say "Peux je", but "Puis-je".
From what I understand, the inversion "puis-je" is formal and so would be considered polite. The "est-ce que" version is considered standard, everyday vernacular without being informal or slangy.
may I and can I are very different in English in terms of degree of politeness (I don't regard them as interchangeable but just alternative options)...I thought it was similar in French with puis-je and peux-je....have I got this wrong?
The difference between "may" and "can" in English has nothing to do with degree of politeness; they are different verb forms with different meanings. "May" is a request for permission, while "can" refers to ability. "May I park here?" asks whether parking is allowed. "Can I park here?" asks whether my car will fit the spot or whether I have the skill to manoeuver the vehicle into the space. The two forms are often confused, and some accept them as interchangeable. As I understand it, peux-ju does not exists in French, even though it seems it should be a logical construction. (Rather like "swimmed" seems a logical past tense form of "swim," when in fact it doesn't exist in English.)
Thanks. I certainly concur with your exposition which fits with what I've been taught (as a schoolboy). However, as you point out yourself, the two forms are accepted by some as interchangeable (the language evolves etc.). I've noticed that in common Australian English of today the 'may I' is used when people want to be very polite or defential. But it seems to be dying out. However, my question related to why DL did NOT allow puis-je and ONLY allowed peux-je as a translation for 'may I'. That I can't understand. What do you think?