Let’s run these down for you:
1. You can install EE on a local development server as long as it meets the requirements. Many folks do this- and the license allows you to have both a ‘live’ site and a non-live development server, so you could continue development on the local box. Or- you can just install straight to the web and turn the system ‘offline’- at which point, only superadmins will be able to see the frontend of the site (see system preferences).
2&3;. EE has a relatively small footprint- what will really matter speedwise is whether your server is tweaked to handle dynamic sites. Most content will be served up from the database. EE does give you many caching options to help tweak performance further. As to web aps- if you’re using offsite services, the speed and reliability of the third party is important to a speedy site. But all of my experiences with google aps have been good.
I know folks have integrated Googlemaps with EE, and there are third party offerings to handle reviews. Photos and videos are no problem- though I prefer to embed vids hosted on other services. As to the forum- we’re using EE’s forum right now, and the membership is fully integrated with the rest of the site. That should be no problem.
If you really want to check EE out before deciding, I’d highly recommend one of the trial options. The hosted demo will give you access to a forum, while installing Core on your own box will give you a chance to look at the code and play with integrating other apps. I’d probably give both a try myself if I had your requirements.