It certainly can be more challenging to find out about a remote employer but you certainly don't want to do a week or months worth of work and wonder if you'll be paid. You definitely want to ask some questions before you send your resume, certainly for privacy sake, you want your resume to go to someone whom might hire you and not to a database that simply collects information.
Not something new, while looking for a full time developer position I am dealing with a huge number of rejections because of aiming too high ...
Research your targets and write a cover letter explaining why you are particularly suitable for the position, say: IF they are interested you can send your resume.
No reply, no resume, no further contact, forget them.
If they reply then you have the opportunity to grill them for some valuable information before you'll send your resume. Know whom you are speaking with and have a few conversations.
If you "just gotta send your resume, we'll call you!" then very politely explain that "you have other calls to return and that you won't take any more of their time".
Remember their first goal: Get your resume and get you in or get rid of you. If you want their computer or someone whom spends 30 seconds on your resume to put you in the trash or treasure pile then do it their way.
If you want answers, to be convinced that time spent with them won't be time wasted then politely explain that you need some more information. Ask for an "Information Interview" that neither involves you sending your resume nor them offering you the job, it involves you interviewing them - they probably will want to know a bit about you, why should they spend their time, but they'll be short of the tool they require to make the decision and you'll have most of the information you need - or just move on.
I get ignored all the time when I ask about the reasons (given that I am just curious and trying to understand what I am doing wrong).
The only chance you have is if they aren't busy, they like to chat, and they are willing to say why you were rejected, and possibly argue with you about whether their decision was correct.
If maybe they might hire you in the immediate future they might feel the need to address your concerns and not brush you off - maybe.
I've called after an appropriate time and inquired if they had any questions and got the pre-rolled response that they would call me if they did. Then a few days later a frantic call that they were very interested and that I should call back at my earliest convenience. I waited a few days and asked for the person but they were unavailable so I simply left a message.
I explained that I had called a few days earlier to inquire about the position and was brushed off, that I was using the information to schedule interviews and to determine if I should leave an open slot for anyone - I took their response as a "no" and now there's an important change of circumstances.
I explained that I wasn't prepared to cancel anyone whom expressed interest for someone whom was initially uncertain and that I am not available.
A few weeks later I got a rejection letter and several months later they got bought out in a hostile takeover and everyone was terminated. The product they made was shelved since it competed with the product being made by the company that bought them out.
So, lucky me.
Question: Can I put a line in my resume "Please tell the reason of the rejection"?
It's not good practice, there not exactly a space for such a comment and it's odd to see that on a resume. It's certainly a stand out feature or a flag. You can stick it right below your name and phone number / email address - they won't miss it.
It might be cause for manually rejecting your resume when there are a dozen other seemingly equal resumes with no such oddity (or expectation that you'll want them to do additional work after they already have what they want).
Otherwise, where can I ask it to ensure that the recruiters are going to see it?
When going through a recruiter they should be local to you and you should visit them, get to know them a bit and put a face and personality on your resume. This person will be the source of dozens, hundreds, (or no) jobs in the near future - best to check them out, and their office. It can only hurt if you know you stink in interviews, then that's certainly where you'll want to improve as otherwise you'll continue to fail near the last steps of your journey.
Note: I apply all the time to remote positions, it goes like (in the best case): application => technical test => interview => rejection.
Choose carefully, interview them after doing your research. Impress them with your interest in both the company and they type of work you are interested in doing. Video chat and see if you get along before you send a resume. If it's just a resume dump into their database and a cookie cutter interview you be working with a bunch of doughmen - just do this, just do that, we'll let you know. Make certain that they are invested too.
If you are an independent contractor take a bit of control over your own company, and remember to smile and be polite when you speak to the customers - the recruiter and to whom they send you. That doesn't mean that you want to show all your cards so they can decide to raise or fold and cut their losses while maximizing your loss.