Some printing companies are asking for the EPS file while others ask for the AI file, ViaVector gives you the EPS, AI, and PDF files.
You can create your own logo for free, online, with an app or with programs like Illustrator, Photoshop, Paint, and Word. In this blog you get an overview of how you can design your own logo.
Opening an SVG file can be done with different software. For some you have to pay, others are for free.
Creating an SVG file from a JPG or a PNG, for example, can be done in Adobe Illustrator. You can also make a (free) SVG image online. In addition, you can have us create an SVG.