randomize selection by weight and skills on sheet

It's possible, but it might be difficult for someone here to envisage exactly what you are after at this stage.

You will also need to define the logic, for example do you prioritise purely on skill level (e.g. as a hypothetical example all available 'level 4' people will be allocated before any 'level 3' people are considered), do you try to balance it out so that within the overall pool of people / skill level, over time it evens out as people selected (or % of available days allocated)? etc...

I recommend taking this step by step, such as considering:
- What format does the input data take? Is it one combined dataset, or multiple datasets (e.g. People and their Skill Level, Dates Available, Dates of Performances)
- Do you do the allocations as one-off exercise or constantly update?
- If you were to allocate people manually on paper, how would you approach this? What logic / judgement calls are you applying?
- What would your expected output look like?

Many on here will likely be happy to guide you through this, but given the requirements you will probably need to drive this by preparing example workbooks and explaining your requirements as it evolves.