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A learner hesitates to ask a question

• A teacher says have有yǒuquestions问题wèntífeel free to尽管jǐnguǎnask问wèn。 — “If you have questions, feel free to ask.” feel free to尽管jǐnguǎn encourages the learner not to hold back in this context.
• Compare feel free to尽管jǐnguǎnto rain下雨xià yǔ，we / us我们wǒ menor / still还是hái shìto go去qù(completed / change)了le。 — “Although it rained, we still went.” The same written word has a different use.

Give permission or reassurance

• Before an action, feel free to尽管jǐnguǎn + verb phrase can mean “go ahead” or “feel free”: have有yǒuquestions问题wèntífeel free to尽管jǐnguǎnask问wèn / want / think / miss想xiǎngvariant of 吃吃chīwhat什么shén mefeel free to尽管jǐnguǎnpoint点diǎn。
• you你nǐfeel free to尽管jǐnguǎnto feel relieved放心fàng xīn，这件zhè jiànmatter事shìto give交给jiāo gěiI / me我wǒ。 means “Rest assured; leave this to me.” Read it as reassurance, not a statement that an action has already succeeded.

have有yǒuquestions问题wèntífeel free to尽管jǐnguǎnask问wèn。

Read the concessive use separately

• feel free to尽管jǐnguǎnto rain下雨xià yǔ，we / us我们wǒ menor / still还是hái shìto go去qù(completed / change)了le acknowledges rain while saying the expected obstacle did not prevent the trip.
• This concessive use can also pair with but但是dàn shì or a similar contrast. A sentence with feel free to尽管jǐnguǎn is not automatically an invitation just because a verb follows somewhere later.

Use the clauses to identify the function

• In have有yǒuquestions问题wèntífeel free to尽管jǐnguǎnask问wèn, the speaker encourages asking. In feel free to尽管jǐnguǎnhave有yǒuquestions问题wèntí，we / us我们wǒ menor / still还是hái shìto complete完成wán chéng(completed / change)了lemission任务rèn wù, the speaker acknowledges problems but reports completion.
• Compare the relation between the clauses. Classifying the second example as broken would confuse a valid different use with a word-order error.

Respect the scope of the invitation

• “Feel free to ask” concerns the stated activity in that exchange. It does not grant unlimited permission to unrelated actions.
• A speaker may later qualify or withdraw an invitation. That can be confusing or inconsiderate, but it is a communication issue rather than proof that the original construction is ungrammatical.

Choose invitation or contrast from context

• To encourage a hesitant learner, use have有yǒuquestions问题wèntífeel free to尽管jǐnguǎnask问wèn。 To acknowledge an obstacle, use a complete contrast such as feel free to尽管jǐnguǎnto rain下雨xià yǔ，we / us我们wǒ menor / still还是hái shìto go去qù(completed / change)了le。
• Identify the intended function before choosing the English wording. as far as feasible; try to尽量jǐn liàng expresses feasible effort; permission-giving feel free to尽管jǐnguǎn encourages an action without hesitation.

Read the full reference: HSK 5 grammar — Adverbs.