Had two implants: does the positioning look ok?

It appears you may have lost confidence in your DDS to seek opinions online. Typically, the full story can only be know from a thorough evaluation of the the tissue, the bone condition, a Scan or CBCT to evaluate any root fragments still in the bone. So an in depth consultation is most often helpful in cases like these to better understand what you had hoped to accomplish with this phase of treatment compared to your overall health and well being. Meaning, it appears there are other missing teeth as well as broken down teeth so some evaluation of a segmented treatment plan vs a full arch solution would typically be warranted. To attempt to answer your question here is my guarded reply: the alignment may be adequate with out a better diagnostic evaluation. Not the worst case but not the best. More information would be helpful for a more accurate reply.

I am concerned with the fact that not only the alignment and space distribution if a bit off, but there are Caries, calculus (tartar) and other dental issues that should have been addressed first. In my office, implants placed when the mouth is as healthy as it can be, towards the end of active periodontal and restorative therapy, not at the beginning.

Your Doctor placed both implants well .Anterior implants are the most difficult to work with .The angulation of implant often detected by the cortical bone width of the bone and aesthetic and many clinical reasons . Looking at a 2D (PAN) may often look odd on the other hand in real life it could be very well placed and success full implant. Also many skill full prosthetic choices can help surgically limited implants to achieve long term success.

The only implant that might be questioned here is the one next to the central incisor, due to its angulation. But without a scan it's impossible to tell. Both x-rays are misleading due to their angulation. The implant next to the bicuspid is not as close to the bicuspid as it looks on the x-ray. But you need to be a professional to understand how that works. The dentist may have angled the implant next to the central incisor just to obtain a better bone purchase (in other words to make the implant bite into denser bone). it is a common practice. The x-ray shows a less bone dense area distal to (behind) that implant, so that would confirm my suspicion. But you not being a professional wouldn't know that. Both implants can be restored just fine. However, there are many other problems in your mouth that also need to be addressed, and they are far more dire than these two implants. Treat those as soon as you can, if you truly care about your health. And thank your dentist for doing a good job with a difficult situation, because the overall space is indeed tight for those two implants. These were not easy to place!