The most important thing would to review its structual integrity. This can be accomplished by removing some of the soffit panels and taking a peak inside. It could be a a rafter tail is comprimised or broken. Therefore, it would need to be fixed by lifting and sistering. (placing dimensional lumber beside the rafter tail and fastening together). Another fix would be to install a column to support the roof. Installing the column would require a stable footing below, (a concrete pad) and lifting the roof to the proper slope and affixing the colum to the sub-fascia board on the eave. The column method would provide the best support over time and combat heavy snow loads, however a "post" would be in the walk path most likely.

The leak and mold are time sensitive. Mold can be hazardous to your health. Dealing with mold properly means removing the sheetock and insulation once the leak is fixed. Don't let anyone tell you they can seal it in place and paint ove it. It must be removed. The foundation work can get vey expensive if you wait too long so don't put that off too long.

Hope this helps.

You can proform both jobs at the same time if you are good at what you do. I have in the past grinded a Grove in the brick chimney all four sides then used a brake to bend a little half inch lip on the top of my flashing metal flashing into massonary Grove then caulked you will never ever have to worry about again in your lifetime Only reason I did massonary work first is because I didn't want to get my shingles all dusted.

What did you decide to do then? Following the proper process would help.

I would rather think your gutter needs a good sealant. If your soffit is sagging, you have some structural issues.Most likely nothing to do with the gutter. 

Our recommendation would be to do the massonry work first and then roofing for a few different reasons.

1.This gives the masons freedom to step and walk on the roof without causing damage to the new shingles. 

2. You will want to make sure the new flashing that is intstalled around the chimney is installed correctly, accounting for any masonry changes and is not damaged due to installation.

3. Ultimately, that the new roof is not damaged and that the warranty does not get voided. 

Call a professional certified roofer who can do a full inspection and report of how to proceed. Professional roofers can bring insite and cost savings others might not. They have years of experience and a trained eye to make sure all problems with a roof are discovered and remedied! Remember - When hail hits an asphalt shingle it often knocks off the protective granule coating. Once the granules are gone, the protective layer underneath is exposed to the elements. Always call a professional roofer!

If actual damage has occurred to the roof, due to hail, there is really no other way to fix the damage, except replacing the roof system.  

Depending on the type of roof that you have, if the damage is minor, you might be able to complete a spot repair, but that also depends on the condition of the roof.  Hail typically falls randomly over the entire roof, so when there is damage, it tends to be all over.  If your roof is older, it might not be in repairable condition, or your roofing material might have been discontinued and have no match available for sale.

I suggest having a Haag Engineering certified roof inspector or a structural engineer evaluate the roof and tell you if you have another option.  

I agree with what Yuri said and would like to add that it is imporatant to have it removed properly so as not to cross contaminate. Mold spores are microscopic in size and easily dispersed if not handled correctly.

There is a bee spray you can mix in a pump up and reach the higher carpenter bee holes. This worked for me.

If the space behind the knee wall is clear from end to end and you install gable end vents at each end then that would keep the eaves from freezing and causing ice dams.Make sure the knee wall is well insulated. You want to keep the heat in the finished area and get the space behind the wall as cold as it is outside.What you need to do is create some convection in there. If you don't want to spend the money for this then you could try a high powered exhaust fan for one of the roof vents and try to get some air movement from that.

The BEST way would be infrared image testing. Only top-tier roofing companies will have them, so may be hard to locate in rural areas. However, the technology is getting older, and the cameras that were $1k, 2 years ago, are around $399.99. Its a solid investment, and requires none of the old, trial and error methods.

I have seen a lot of great DIY carpenter bee traps that fill up with bees. I have friends that say the traps keep them out of the house. 

https://www.pinterest.com/explore/carpenter-bee-trap/

The best way to fix and resolve ice dams is actualy proper isulation in the attic space. Next is proper ventilation. Both intake and exhaust. These are critcal but rarely done correct and very costly and hard to do rero. 

If the above are not done then a good qulity ice melting system is best. Either a commecial grade heat cable/heat tape or an ice melting system such as a heat panel.

Never use a continous watage cable as they are not safe or effecient. 

Only use a self regulating cable as they are safe and effecient. 

You will want the cable in the gutters and downspouts first, the next step is cable in the valleys and lastly weaved on the roof.