Not sure since I got my Internet from Paraiso (whose access has been upgraded and no longer requires constant logging in). Tetshuro is around so my guess is ya, his service is probably still running. I very robust steel structure was being constructed at Naito - a frame for a canopy on the patio I assume, so I think a newly renovated Naito's is on the way. Half the retail space in that building has been rented to the Italians from Paraiso and they have opened Martini Bar in the nicely renovated space. It is a bar and restaurant but I haven't eaten there. My guess is the food is prepared across the street by Gemelli's.
Another supermarket in San Pedro that is very convenient is Zaglul. Before I got familiar with San Pedro I always went there because it is right on the main drag after crossing the bridge, making it impossible to get lost if you are driving yourself. You go halfway around the rotary after the bridge (i.e., straight through) and Zaglul is about 8 blocks up your left. They have everything you need, including cell phone shops, Western Union, and 3 different ATM's. Typically I go to Iberia because that's what my novia prefers. I think prices are the most competitive there although I haven't really compared. Plenty of options in San Pedro, but as noted, one has to get himself there and back.
If you do drive to San Pedro and you are a bit adventurous, check out the Malecon in the evening for a real Dominican Experience.