My question is this: is it a good idea to have a complete facial hair removal with laser at the early stages of transition?== Yes, the earlier the better. You'll thank yourself later when you don't have to put thick makeup on just to cover the beard shadow.

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Will my transsexuality be obvious after the removal? Is it very conspicuous and obvious if someone is not in en femme? == being trans won't be obvious at all. That isn't a conclusion most people even think about. (unless there are other indicators) My hair was very dense and thick when I started...always obvious beard shadow even after I just shaved. I don't have much hair above my jawline anymore, and I've hinted a lot with a couple of my family members about it. People don't notice subtle changes over a long time as much as they do great changes over a short time. A lot of people just don't see what they don't want to...or expect to...see. Most will just think that you're clean shaven. (Or if they do suspect, most won't say anything at all unless you bring it up)
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==Some things about hair removal can be conspicuous though, but there are ways that you can minimize it. Your face can be red and bumpy, and a bit scabbed for a few days afterward. (some areas of the face react more than others. Some days are better than others.)
I've been getting 2 hours of facial electrolysis every week for the past 2 years. I purposely schedule it for Friday night to minimize what shows. I have a little gruff the last couple days of the week while it grows out (perfectly normal for guy-mode) (which has gradually diminished over the past 2 years), and (on bad days) a red bumpy face during the weekend after treatment. Usually I'm healed back close enough to normal by Monday that at worst people might think I'm just breaking out in a few pimples.
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==So far, it doesn't appear that anyone has noticed. I'm still not out at work, but I hide all of the other indicators pretty well. I probably don't need to do electro on Friday anymore, but I play it safe anyway. No matter how you choose do it though, I wish you the best of luck.