How many requests can EC2 t2.medium handle?

Realistically, there's no way to tell because it depends on what your code/page/environment is doing on that server. The best way to figure it out is to test it. Bring the server up; throw requests at it and measure.

There are many other instance types. The only thing unique about the T series instances is that they run on CPU credits which means that performance may vary if you push the instance too hard. For larger, constant loads I would recommend other instance types. You can monitor them if you do decide to use a T instance.

Note also that the number after the instance type is the series and higher is generally better. So I'd go for a T3 rather than a T2 if it was my choice. But again, in this case, for a high performance website you're probably going to find that a M (general purpose), C (more CPU), R (more memory) series instance is going to be better.

It's hard to answer this question without knowing what requests are doing exactly. Generally speaking, 150 requests per second (rps) are quite a bunch, and unless they are really easy to serve (or cached), such a small instance might struggle.

One suggestion might be to run a load test (use "ab", "jmeter" or LoadImpact which is SaaS) with peak load and see how it performs. This is the most realistic measurement you can get.

As other posts flagged this is hard to predict It depends on the load caused to the instances by the requests. This, however, is a nice case for autoscaling, If the applications hosted supports it you can create an AMI with the software and the configuration required and set up an autoscaling group. Then you can place automatic scaling policies based on CPU usage or, once you learned the limits, based on the network in. Put sensible limits to the group so it won't scale beyond the number of instances you're willing to run in parallel, and also put downscaling policies or you should manage the excess manually. This, however, requires a bit more skill and the application must be designed in a way that can scale horizontally gracefully.