Kaivan Kiai, DDS

If you have enough bone to hold an implant , the implant option is always the best.  Since we are dealing with front teeth, it's always best to match the color for cosmetic reasons.  

The front tooth can be pulled down through braces if you have enough root structure, healthy bone and root.  Orthodontics and a new crown can make this case look really good granted you qualify for it.  You need to get both an orthodontist and a general dentist opinion, working together in this case to get you the best results.

Crossbite can be fixed with Invisalign.  It's hard to tell based on the picture you provided if Invisalign would be the best treatment option for you or not.  There are many factors involved in orthodontic treatment.  You need to have a full exam and some xrays to evaluate the best option for you.

The way veneers look is much more aesthetic than filling on front teeth.  White fillings look for mat and veneers are more shiny which resemble tooth structure.  The color on fillings will change over time and it will be obvious that you have something on your teeth.  To address your braces question, if you're getting orthodontic work done, you need to hold off on the venners until you're done.

There are a few reasons why a crown would keep coming off.  One is if there's not enough tooth structure underneath to retain the crown in place, another is the type of cement used.  One more contributing factor is your bite.  If you have a deep bite anf keep biting hard into the crown then the crown will come off.  You need to have this re-evaluated by your dentist and look at other options.