You did not supply actual dimensions for the new door size, new frame rough opening size, or the old frame internal dimensions. As such it is difficult to give specific advice. That said here are some basic suggestions.
1) Before fitting the new frame within the old frame do remove the doorstop molding from the old frame.
2) Remove any and all casing from around the old door frame. You will be adding new casing from the new frame all the way out to the existing wall. By nesting the frames the way you want to do this casing will end up wider than your existing casing. You may be faced with using some pine boards to make up the casing boards.
3) Check the width dimensions of the outside of the new frame to the inside dimensions of the old frame. If this overall difference is larger that thickness of one or more standard pine boards (in US this is 0.75 inches thick) you should add a board(s) to the inside of the old frame to fill up part of the space. You will want to leave a free space in between each side of the frame of ~0.8 to 1.2 cm to allow for adjusting the new frame to plumb.
4) Check the height dimension of the outside of the new frame to the inside height of the old frame. If the overall difference is more than the thickness of a standard pine board you should add board(s) to fill up part of the space. You will want to leave a free space in between at the top of the frame of ~0.8 to 1.2 cm to allow for adjusting the new frame to square and level across the top.
5) Use tapered wedge pieces of wood in pairs in between the frame sides and at the top to bridge the gap between the frames at the points where you will nail the new frame into place. These tapered wedges can be adjusted by pulling them apart or together (end to end) to adjust the gap as you plumb, level and check the new frame for square. Once the fit is correct nail through the new frame and wedges and into the old frame to secure the new frame in place. (If you had added gap filler pine boards in between these nails will be going into those boards first before poking through to the original frame). These wedges can be purchased ready made or you can make your own.
6) Once the door is hung and has a good fit it is time to install new casing over the edge of the new frame all the way over to the wall edge that was previously covered by the old casing. In all likelihood this new casing will end up being a custom casing that you will make from trim boards. However there is a possibility that you may be able to locate a suitable material that you can re-purpose as a casing such as some styles of wide baseboard.
Note that before you start on this endeavor you want to check the width of the new jamb sides as compared to the old frame. If the old one is wider you will have to fur out the new frame with jamb extensions so the width is very slightly wider than the existing jamb. This is so that when you install new casing boards that the trim does not rock on the edge of the old frame.
An opening under the building code would typically be a door or a window.
If you have a gas leak, the dryer vent nearby doesn't significantly increase the hazard of the gas leak, because the hazard of a gas leak is massive.
On the other hand, blowing hot moist air on a piece of equipment is more likely to create maintenance issues and routing a new installation is typically pretty easy, it's probably worth a little extra trouble to avoid venting directly onto the meter.
Best Answer
If you build the pad with concrete you may want to consider not making it out of a solid block of concrete. Instead form it up to create sides and a couple of steps as necessary. But then fill a large portion of the inner area with sand so that the top of the landing is 4 to 6 inches thick. A little re-bar in the sides and folded over to embed in the top can help keep the thing together if it cracks due to frost.
If you do live in an area with frost getting deep into the ground you should consider adding corner holes down into the ground (with re-bar up into the step portion) that can act as posts down below the frost line so as to minimize the heaving effect that can make a floating construction move around during the year cycle and also settle into a off level state over a series of years.
Wood can offer an easy alternative but you have to determine if wood has a look that you like. Also wood may require replacement in 15 years or so depending upon materials and conditions. Finally with wood, if a frost zone, it is a good idea to build it on treated posts that you bury to a depth below the frost line.