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Hello - I hope my answer will help point you in the right direction.
The reason you're having a hard time getting clear information is because there are hundreds of companies saying their window is the best. There are probably millions of different features you can choose to have for your windows and in price ranges from $169-$1200 (per double-hung window).
I've been in the business for 15 years and have seen many different window products from many different dealers and manufacturers. This all comes down to: "what's important for you and your home?" If you want a strong warranty from a company who has a full-time service department to give you piece of mind and service your windows should needs be, or are you looking at only those companies who offer true wood interior windows that you can paint or stain to match the home decor? Whatever is your hot-button, then that's where you want to start.
I would recommend you first choose how you want your new windows to look. Wood-interior with vinyl clad is only offered by certain companies, while there is a vinyl woodgrain finish to give you similar results without the maintenance. If you're only looking for a white interior and don't want the maintenance, a fiberglass or vinyl window would be the best choice from what is offered in the market today (vinyl will be less expensive - not necessarily cheaper quality). If you are going to change out a window to a french door and a door to a window, then you WILL NEED to find a contractor with some carpentry experience. Some companies will tell you upfront that they do not handle those sorts of remodeling projects due to the complexity and time it would take to get it complete.
Unfortunately, we won't be able to personally help you with your project as we work in the New England Area. However, if you wish to talk further, please feel free to email me at: email@example.com and I'll be happy to let you know our prices for what we offer so you can compare and hopefully find a similar company to do the work for you near the Austin area.
Get your roofer back out there. Course of shingles above the window need to be pulled, self sealing flashing, drip caps, and counter and step flashing are going to be required here.
This is a flashing issue as the window connects to the mansard roof surface.
Condensation and a leak are two different and very noticeably different (i.e. volume) things.
Flashing and roofing on Mansards can be tricky but is sounds very much like a roofing issue.
For a broken window (or leaking seal in multi-pane unit), for a standard roughly 2x3 foot window, can run from low of about $75-125 for single pane to more like $200-300 range for triple pane, depending on construction and any special ultraviolet or heat reflective coatings. If a removeable window unit, of course cheaper to remove it and take to replacement glass place then have them come out, measure glass size, order glass unit, then come back to install.
If taking in yourself, commonly they can do single-pane in an hour or two, but count on a week or so typically for sealed double or triple pane unit to come in, so you will have to seal the opening in the interim. That is an advantage of having them come out - they measure and determine type of unit on first visit and can seal with tape and plastic sheeting (if you have not already done that), then come back with new unit and install a week or two down the road - but you are not stuck with an opening in the wall for a long time.
Much easier to scratch and typically not as good a finished quality as compared to glass.
Benefits are the resistance to breakage as mentioned by LCD. Any glazing shop should be able to re-create that panel.