You can work around the Flash video issue for now with Skyfire on iOS devices. It's not great, but it's something. (Yes, iOS browsers do exist beyond Safari)
As for the apps, it would depend on what they do. Some may not be touch aware and simply wouldn't work. Others may need a more powerful processor then the ARM chip in the iPad and other mobile devices. It's all a crapshoot right now. Apple did attempt to let Flash on the iPhone initially, by coding in support for browser plugins and everything. The fault for Flash not being on iOS is Adobe's, not Apple. Apple set a minimum quality bar that Adobe never passed in 3 years of attempts, and Apple finally put their foot down.
From All Things D in 2007 prior to the iPhone launch but after the announcement:
Q: If the iPhone’s Web browser is so good, why can’t it play video on Web sites I visit?
A: At launch, the iPhone version of the Safari browser is missing some plug-ins needed for playing common types of Web videos. The most important of these is the plug-in for Adobe’s Flash technology. Apple says it plans to add that plug-in through an early software update, which I am guessing will occur within the next couple of months. However, a separate program included on the iPhone can play a limited selection of videos from YouTube, and the phone can play videos you purchase from Apple’s iTunes store, and certain videos you create yourself.
And this was still in the works even in 2009:
“It’s a hard technical challenge, and that’s part of the reason Apple and Adobe are collaborating,” says Shantanu Narayen of Adobe. “The ball is in our court. The onus is on us to deliver.” - February 1, 2009
Adobe failed to deliver. Apple moved on. And Google embraced it as an attempt to have one more checkbox feature over iOS devices, leading to poor experiences for Android owners trapped in a platform battle. Google normally pushes for an open web, except for Flash.