Yes. Or superficial phlebitis. Need ultrasound.
Unlikely. A pink tender cord is more likely a small superficial vein which is inflammed, otherwise known as superficial thrombophlebitis.
Need to check it out. Although I agree with everyone that it sounds as though it is likely to be a phlebitis or a superficial venous thrombosis (svt) which is also called superficial thrombophlebitis, as much as 24% of the time that someone has an svt there is a DVT in conjuction with it. No well to tell for sure clinically, you need an ultrasound.
Probably not but... A palpable tender cord on the inside of the leg is more likely superficial thrombophlebitis. It's less serious, but calf pain and leg swelling are concerning and should be investigated immediately to prevent a deep vein clot from migrating to the lung. With either of these symptoms you should visit your dr.