I don't see any real issue with this for the fresh mango, subject to suitable inspection and rotation. Not that unusual for mango to need a variable amount of extra time to complete ripening after picking, so as long as you're checking ripeness and intake, and monitoring it, so you use it when it is ready and don't let it go too far, then this should be fine.
You'll doubtless know the varieties your handling far better than I do, so you'll already be aware that not all varieties will ripen at the same rate post-harvest, and you'll need to set your system up to monitor, rotate, and process accordingly.
For the dried mango, I see plenty of ambient dried fruit - the question is perhaps how "dry" is the fruit in practice? i.e., is moisture / aw your control for preventing growth (be it spoilage or pathogenic), and is this achieved by your process and storage conditions?
For the testing of product in storage, I don't know how regularly you'd need to do this and it's difficult to speculate without access to your full historical data. If you've already got lots of analysis showing that the shelf life and storage conditions are working, then pathogen testing every batch every week may be overkill.
Also may be useful to consider - what do you believe to be the limiting factor for your product shelf life? Is it pathogen growth rate? I'd be a bit surprised if this is the case for a dried fruit product, but again you know your product better than I do!
For the testing of production on the day, analysis type and sampling frequency is perhaps going to depend on the scale of your process. It's not a material that you'd easily get a single representative sample from (as it's definitely not homogeneous) so you may want to look at statistical sampling approaches. Personally I'd be inclined to add in a couple of spoilage/indicator tests (perhaps yeasts, moulds, TVC or similar) at least initially if you don't have data on this at present.
Do you handle any allergens on site? If not, then I'm not sure testing that frequently would really be needed?
For the raw material, yes, Brix, firmness, visual inspection for certain. You may also want to add acidity (since Brix/Acid ratio is going to give a reasonable indication of sweetness), and do both Brix and Brix/Acid ratio on the stored raw materials to monitor for ripeness, i.e. how close it is to being ready for processing.
Pesticides for every intake would be unusually frequent IMEX, but again you know your raw material supplier setup best, so if this is the appropriate way to manage the risk then you could start there and always look to reduce frequency if the data supports this. Alternatively, a once per season per grower approach might reduce the frequency (and therefore cost) but still provide sufficient data. If you've got good relationships with your growers then I'd also suggest a collaborative review of their pesticide application records may be a good way to reduce the need for testing whilst providing (hopefully) positive assurance.