Interview questions for Entry level trading position/intern

Hi everyone,

I've always been interested in prop trading and have been doing my research for the past couple of months. I'm more interested in trading at a lower tier firm like Trillium, FNY, Group One Trading than the more competitive ones, since I don't have the traditional quant background nor that most higher tier firms (Citadel, Jump, JSC) look for.

A little about myself: I'm going into my senior year of UG at a super nontarget school (CUNY and not Baruch) majoring in finance with a 3.7 GPA. Currently, I'm doing a FP&A intern gig and registered for the December CFA lvl 1 exam. I've had day trading experience in the past and when I use to day-trade and traded strictly on TA (RSI, MACD, dojis, support&resistance line, to name a few). Unfortunately, I do not have any experience developing an algo and testing it. With that being said, here are the questions I have for the current traders out there:

1. Do any of the lower tier NYC-based trading firms accept trading interns during the spring?

2. Any tips to getting the first round interview, given my background?

3. What books or online material should I read/practice to prepare me for the interviews?

4. I'm currently practicing the double digit multiplication, and was wondering how fast I should be able to reach a correct answer? (10-20s?)

Thank you.