It depends on what you want your user to do with the map. I made suggestions in the "Summary" portion below.
What is considered a good size and position? (minimum)
Honestly, this depends on what you want your user to do with the map. One thing you always need to keep asking yourself is What is the purpose of this page?. Is it to contact you or to see what's around your HQ? By the looks of it, it seems like it's for them to get in touch with you about your goods and services.
If you want them to be able to pan around and see the surrounding area (or maybe look for other stores/stores that carry your brand), you should make it larger and more of a center piece on the page. If you want to just use it as a geographic reference so people can understand where you are located in the world, the way you have it currently is good as far as size and location.
Static or dynamic map?
I agree with you in saying that a dynamic map is the way to go as it gives the user more freedom to pan and zoom around and see the area around your HQ, but you need to ask yourself "What will my users gain from panning and zooming?". If you just want to put it in because it's a cool feature, don't. That's not smart and your users will get lost in the map instead of doing what they originally came to the page to do, which is contact you about your goods and services.
How to put "get directions" button?
I would make the directions part of your address. It looks like you have your address posted up at the top. You should make that a clickable link that takes people to the exact location of where your store is located, like the way this link does for London. Just because it is something to do with a map, doesn't mean it has to be ON the map. Metadata around the map is just as important.
If you want to reinforce them coming to your store, you should make the pop up clickable and put a link in the pop up window that says something like "This is where we are. You should come say hi!". Right there, this gives your users enough curiosity to click on the link and see your location in Google Maps itself. Even if you don't want to include a witty phrase, you can at least put the full address in that has the same Google Maps link attached to it.
Also, I would consider removing the icon all together. Icons can sometimes be confusing to some users and if you have the directions in a link, that will be sufficient.
So in summary of everything, there are a couple pieces you need to think about when making this map.
- What is the purpose of my map?
- What do I want the user to take away from this map while their on this page?
- How much interaction does the user really need?
- Do I need to include a logo for directions?
Based on my years as a cartographer and based on the situation, I would do:
- A dynamic map where it is currently located on the page
- Limited to no pan and zoom
- A pop up window with the address
- a link to the Google Maps location