Pete's seven year old answer is just as relevant now as it was in 2011. None of the limiting factors of their API has changed since then, so this is essentially an extensive reiteration.
The Interactive Brokers API is not suitable for high frequency trading execution. However the main reason that this is the case is not necessarily what would come to mind when thinking of this problem.
The data feed itself is not fast enough nor is it optimized for high frequency trading, nor can you even have access to enough streaming real-time data to make HFT-type trades (even if we completely disregard latency). From the "order limitations" section on the Interactive Brokers Docs, the following is stated:
Aside from the TWS API's inherent limitation of 50 messages per second implying a maximum of 50 orders per second being sent to the TWS, there are no further API-only limitations. Interactive Brokers however requires its users to monitor their Order Efficiency Ratio (OER) as detailed in the Considerations of Optimizing Order Efficiency IBKB article.
Additionally, please note IB allows up to 15 active orders per contract per side per account.
In fact, the better answer to that question also states something very crucial to take note of (and something that hasn't changed in the past 7 years). And that's that the order cancellation fee is EXTREMELY tough, and a major if not one of the most important aspects of a high frequency trading strategy is how it reacts to changes in the order book. High frequency traders cancel tons of their orders, and a fee as large as $0.12 makes any HFT activity totally outlandish.
The fact that Interactive Brokers runs Timber Hill is also something important to consider as the other answer stated however it isn't as big of a factor as the 50 messages per second limitation and order cancellation fees.
Question 2: What is the best HFT broker to use with a MM strategy?
Any broker that has you sending and receiving information through the internet is going to be too slow period.
HFT is a game dependent on hardware, speed and how close your are to whatever exchange you decide to use. Every single other player in the field will have better hardware and will be closer.
The only retail-ish broker I know of that can potentially provide the co-location you need is Lime Brokerage.
Edit #1 to include a third question:
Question 3: Can it still be profitable to trade with a strategy MM via IB API instead of NASDAQ directly?
For the most part, the answer is no. Even if the feed the Interactive Brokers API provides was suitable for market making activity, latency wasn't an issue and their cancellation fee did not exist you would still run into problems.
The capital requirement for being a market maker isn't just some arbitrary value: the number exists for a very important reason!
The NYSE had an empirical basis for this number. The NYSE Market Maker Capital Requirements website has information regarding how much is needed to be a market maker on their exchange. The minimum net capital is \$100,000, plus \$2,500 for each security registered as a market maker, with the exception there being that if the market value is under \$5.00 the number is \$1,000 rather than \$2,500. Note that these values are for Market Makers subject to the Aggregate Indebtedness Requirement, whereas other market makers subject to the Alternative Net Capital Requirement need a base of \$250,000 and 2% of aggregate indebtedness.
Also see: Key. SEC Financial Responsibility Rules
The Securities and Exchange Commission's (SEC) 1 uniform net capital
rule (15c3-1) and customer protection rule (15c3-3) form the
foundation of the securities industry's financial responsibility
framework. The net capital rule focuses on liquidity and is designed
to protect securities customers, counterparties, and creditors by
requiring that broker-dealers have sufficient liquid resources on hand
at all times to satisfy claims promptly. Rule 15c3-3, or the customer
protection rule, which complements rule 15c3-1, is designed to ensure
that customer property (securities and funds) in the custody of
broker-dealers is adequately safeguarded. By law, both of these rules
apply to the activities of registered broker-dealers, but not to
unregistered affiliates
TL;DR: Market Making is not something to pursue if you are on a strict budget: Minimum capital requirements and the infrastructure required make it quite the expensive venture.
You cannot be a market maker routing your orders through a market maker, it would be "cheaper" however it would also not be market making.
