Randomizer

When you say "a participant may only get one type of questions" do you mean you only want them to get one type? In other words, you want randomized choice between group A questions and group B questions? And whatever type they get, it should all be from the same group?
If so, Put all the A questions in a Block, and all the B questions in a different block. then randomize the blocks.
On the "50:50 ratio"
Are you doing a specific number of responses? If so you can set quotas so you only get 1/2 of one type and 1/2 of the other.
On the "Provide an A-type question at least 6 times...out of 15 questions" - If you have each question Q1A and Q1B as a different block, you could use Branch logic to count how many A's they receive by the time they get to Question 9. If they have less than 6 A's up to that point, you could use a variable to force A's for the last 6. But that would taint your answers to those last six A questions.

You can add probability using Qualtrics's randomizer. For example, if you want A to be shown exactly 40% and B to be the rest 60%. Then you can assign 2 A's and 3 B's.
Alternatively, you may set Quota's to control the ratio. Hope this helps!

You can set an randomizer and embedded data at the top of the survey flow as below:
This will randomly assign a group to each respondent(50:50 as per the selection).
Now on each question, you need to write a logic as below: