[Windows 10 Mobile] GoodDayToDie:
I'm going to assume you're asking primarily about Windows 10 Mobile (W10M), not the legacy Windows Phone (WP7.x and WP8.x) OS family. Although the underlying OS is very similar between WP8.x and W10M, the answers to some of your questions change.

Yes, all W10M devices can now be jailbroken/rooted (we don't have a single term for it right now; if you say "rooted" people will know what you mean). On W10M, there are two critical elements to rooting a phone: the ability to run unsigned (or at least non-MS-signed) code outside an app sandbox, and a way to launch an application with high privileges. We can now do that for all W10M devices, including WP8.x devices upgraded to W10M.

As others have said, the extensions are .xap (Silverlight / XNA apps, used for WP7.x and some WP8.x apps, still supported on W10M), .appx (WinRT, used for W10M and some WP8.1. Used for "Universal" Windows [Phone] 8.1 and Windows 10 [Mobile] apps, such as W10's "Universal Windows Platform"), and .appxbundle (just a collection of .appx files and their various resources / requirements). As with .APK files, they are just ZIP archives and can be opened by 7-Zip or anything else that knows the format (unless they are DRM-encrypted, which ones from the Store often are).

Yes, W10M supports sideloading. It's actually easier to enable on W10M than it is on Android (it's an easily-found option in Settings). By default you're limited to 20 sideloaded apps at once, but there are ways to bypass that.

Against external attacks, W10M is extremely secure. There have been no easily-exploited vulnerabilities (like Stagefright for Android), so far as I know. The app store is also better curated that the Play Store, and you can fully control the privacy settings of individual apps. Also, unlike with Android, Windows phones continue getting updates long after release, especially if you use the free preview / Insider programs to get your updates before your OEM or mobile operator bother to approve them (which sometimes never happens, both on Android and Windows, but on Android the only way around that is to go with a custom ROM; on W10M Microsoft makes it possible to still get updates).

Very much depends what you mean. In one sense, yes, of course; all W10M executables (both system and app) are EXE files (.XAP files may contain only a DLL that is loaded by a system EXE; newer apps include their own EXE). EXEs intended for desktop PCs generally won't run, though, because they use the x86 or x64 instruction sets, and the phone uses the ARM (actually THUMB2) instruction set. These are completely different "languages", and ARM CPUs cannot understand x86 machine code without an extremely slow interpreter in the middle. Additionally, the phone does not support the "Windows desktop" user interface at all, so you can't run any graphical programs (except "immersive"/"Metro-style"/WinRT/whatever-they-re-calling-it-this-week) ones. Command-line interface programs can be run (if they're compiled for ARM processors, and the phone is jailbroken) but there's not (yet) any translation layer for running x86 apps, even command-line ones, on the phone.

A more consistent UI across phones. Better control over when apps run and what they do (which often gives better battery life). Much better update support, even for "unsupported" phones. Pretty good performance even on really low-end phones; a cheap Windows phone will run much better than a cheap Android phone. Better security. Higher-end Lumias have some of the best cameras ever put in phones. Continuum for Phones (connect to a real monitor, and optionally USB keyboard and/or mouse, and run apps on a bigger screen). Easy access to pre-release builds, if you like trying out the bleeding edge features and such. Integration with all the Microsoft services (Exchange and Office365, Skype, OneDrive, etc.), although you can still use Google mail/calendar/etc. Tap-to-pay with high-end Lumias. Many apps can be used on both PC and mobile Win10 but you only need to pay once. Easy to re-flash your phone if something goes catastrophically wrong (commonly called "soft bricked", i.e. you can't even factory reset anymore), although they don't get into that state any more often than Android phones. Specs-for-specs, Windows phones are often cheaper than Android ones. Doesn't send a bunch of personal info to Google (of course, maybe you don't trust Microsoft any better, but at least their primary business isn't advertising).

... there are lots of reasons, just as there are lots of reasons to prefer iOS, or to prefer Android. Without more info about what you find important in a phone, it's hard to guess what stuff you'd care about.