Can one or two emoticons be used in a PhD Thesis?
I highly value humor and love to entertain whenever I can. In formal writing, I would encourage you to go ahead and write something that you think would be funny. Then reread it. Then reread it again. Read it aloud. Read it silently. Read it again tomorrow while you edit it. And read it again. And again. And again. Imagine reading it out loud to the people with the least sense of humor you know. Imagine reading it to a person with a furrowed brow, in a bad mood, who is trying to find anything they can to rip apart what you have laid down, to find a reason to cast it aside as useless junk.
Then read it 10 more times, as any good writer must inevitably do. Now imagine reading it again in 10 years (if you are lucky and what you've done turns out to be of use).
Personally, I have found that after the 20+ time I've read something, it isn't even funny to me anymore - and I think I'm hilarious! But even the best jokes I've ever told never landed 100% of time, or to 100% of the audience - and in formal writing I don't even know who the audience is - they might speak my language as a 2nd (or 3rd or 4th) language.
Being stubborn, I like to write humor into anything I make. But after the 20th read through I realize it just isn't funny any more, even to me - and if that's how a reader would feel who doesn't get or appreciate the joke, it just isn't worth it any more to me to include it. I'm basically writing a technical instruction manual, and there's a reason those things aren't really funny - you are supposed to read them and refer back to them repeatedly, and jokes get old fast.
If I really like a joke, I'll save it for when I can make it in person, in a talk or in a presentation, when I can personally hear the laughs (or gauge the room and know to skip it entirely). Or I'll be funny on a website like this so I can wallow in a mass of glorious unicorn points.
But in formal writing like a thesis or important research paper? Well, you decide after you've read it for the 30th time if it is still worth inclusion, or if that emoticon makes you smile - or if you want to poke it in its tiny little semi-colon eye.
Many writers make very effective use of humor in their writing, and this extends to technical and scientific writing as well. Donald Knuth is one author I can think of who does this extremely well, which is one of the many things that makes his books memorable and enjoyable to read. So I think there is definitely room for some small self-deprecating remarks in a PhD thesis, if this is done in good taste and in (great) moderation so that it doesn't distract from the main, serious (unless your thesis is about humor or comedy ;-)) content.
With that said, I am going to challenge you to make funny jokes in your thesis without using emoticons. If you think about it, the emoticons don't really add anything other than clarifying that you are making a joke, and in that sense they are a kind of humorous crutch. A truly good comic writer would never use one, since it simply won't be needed. So why don't you try to write humor like a pro and show that you take your jokes as seriously as the rest of your thesis? ;-)
(yes, I know I didn't follow my own advice, but I guess I like self-referential humor too much to be able to resist the temptation...)
Yes, they're considered unorthodox. As they would be in any piece of formal writing in or out of academia. In fact, you may already be on thin ice by "making fun of the author" in a footnote.
You want people to read your thesis and be impressed with the work you did. Your goal is not to make people think you, the author, are funny or cool (if jokes in your thesis would even accomplish that, which they wouldn't).
Edited to add: If you do use humor in academic writing, it's much better to make a relevant point in a funny way than to make humorous asides. The first rule of writing anything is to never waste the reader's time, so anything humorous in a document that is explicitly not meant to amuse people had better also accomplish something relevant to the actual purpose of that document.