legally yes, because "best" is subjective. For example it could be the best website from your 3 years old daughter point of view
best site, best domains, best whatever, ..... Doesn't that look more like spam then something serious? It would only make you look unprofessional imho.
Yes you can, it's your opinion that you are the best and is protected under free speech laws. It looks incredibly tacky though so I wouldn't do it though.
Well, aside from some random opinion, there is a little bit of legality involved here, and it works to your favor (disclaimer: I'm not a lawyer, and this only applies to US law) There is a legal difference between purporting fact and something called "sales puffery." Puffery involves any exaggerated claim in the interest of sales or related benefit and is not considered enforceable per the language you use. Calling something "the best" or "second to none," etc. cannot be legally enforced. However, if you make a specific claim about the performance of the site (e.g. "#1 in online ____ slaes) you have to back that up. I guess what I'm saying is that your claim is a perfect illustration of "puffery" and therefore is not subject to any foreseeable legal enforcement, in my opinion.