When using 尽管 as "feel free to", do I always need to use it with 你? Can I omit 就? Can I omit 吧?
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Some examples can be found in Chinese Grammar Wiki：
大家 有 话 尽管 说 。
Feel free to talk if you have anything to say.
有 什么 问题 尽管 问 。
Feel free to ask if you have any questions.
有 什么 事 尽管 找 我 。
Feel free to ask me for help if you need anything.
这些 饮料 是 免费 的 ， 尽管 喝 。
Feel free to have these drinks. They are all free of charge.
想 吃 什么 尽管 点 ， 我 请客 。
Feel free to order anything you want. I'm buying.
And to answer your questions:
do I always need to use it with 你
No. You can say: 让他有问题尽管问我. And from the example you can see that it can also used with some other pronouns, or with the subject omitted.
can I omit 就
Not in your example sentence, but it can be used without 就. See the examples above.
can I omit 吧
Yes. And "吧" can be omitted from your example sentence.