You can still run successful tests. Here's a handy calculator you can use to approximate a required sample size for your test: http://www.evanmiller.org/ab-testing/sample-size.html

Well it depends on your conversion rate. But assuming it's ~few percent, then yes it will be hard to measure anything other than very very large effects in conversion rate unless you're willing to wait quite a long time.

You can measure more upper-funnel things though like I said in the GP, which can be very helpful, especially in combination with qualitative feedback, although this depends on what exactly your business is...