Assuming that you have all required visas, crossing the border is just a matter of crossing the bridge.
Taxies are ofcourse allowed to cross, that's what taxies do for a living... There is also a train, that could be faster if traffic is heavy on the bridge.
In really heavy traffic, there can be cars waiting in line all the way across the bridge. My only crossing took 1,5 hours from Paraguay to Argentina, and 10 minutes from Argentina to Paraguay. So it is impossible to predict how long it will take for you
Don't forget to get you exit stamp in Paraguay and entrance to Argentina, or the guys in the airport will get very mad (or happy for the monye you will have to pay them)
Carmenere 007 has a good post regarding Paraguay. We caught the train from Encarnacion to Posadas. I think we paid around 7000 guaranies. The train is a shuttle service starting around 0700 and finishing around 6 pm maybe later. It only takes 10 minutes for the trip. Immigration officials for both Argentina and Paraguay are on the Argentina side at Posadas. If going to Paraguay from Argentina you will need to check visa requirements especially entering overland as the Airport in Asuncion is the only place where you can get a visa on arrival. Both Posadas and Encarnacion has plenty of taxis. Check out Fauna Paraguay website for tours within Paraguay.
i'd also recomend the international train shuttle instead of a taxi...
I agree with the posts above. While you can probably take a taxi, I would advise crossing on a bus. Plan PLENTY of time for your border crossing. I have made it in 20 minutes in the middle of the night, but it can often take upwards of 2 hours. Once, I almost missed a flight out of Posadas because the crossing took SIX HOURS. I have never taken the shuttle train (I usually drive myself), but it would certainly be worth looking into. Keep in mind, bribes are common on the bridge crossing. You must make sure you get an entry or exit stamp on EACH side of the bridge (two stamps in total per crossing). The border guards like to "forget" to stamp, then charge you a bribe. If someone tries to bribe you, refuse to pay and laugh it off. They'll let you go. The border is amicable and you're unlikely to encounter any actual issues.
Hello Steph. Our experience was that we caught the train from Paraguay at the Encarnacion railway station and took the 10 minute train ride across the bridge. We received the exit stamp from the Paraguayan Custom Official and received the entry stamp from the Argentinian Official both at Posadas. Both custom officials sit next to each other at the same table. After you receive your entry stamp another Argentinian official scans your bags through an Xray machine and we walked through to a taxi rank and departed for the Posadas airport.
Sorry Steph - I should have added - re the entry Visa into Paraguay - We are Australians and we were told by the Paraguayan Embassy in Canberra Australia that we needed a Visa prior to travel as we were crossing overland borders at Ciudad del Este (Foz do Iguacu Brazil Border) and at Encarnacion (Posadas Argentina Border). We were told the only place to purchase a Paraguayan Visa on arrival is if you fly into the the capital Asuncion for $100USD - we walked past the Visa booth after we got off our flight from Ciudad del Este so it does exist.
At Ciudad del Este we received the Paraguayan entry stamp from the Custom official and the Paraguayan exit stamp at Posadas.
Note: as the Brazil/Paraguayan border is open we received the exit stamp from the Brazil side and we could have easily driven past the Paraguayan border post however noting other peoples comments - If we had arrived at the border gate to exit into Argentina without first having had an entry stamp we would have experienced some troubles. Despite what locals, taxis drivers etc will say to you "no stamp needed" insist you stop and get the entry stamp. We did see one person trying to enter into Argentina and without having first received a Paraguayan entry stamp and there was a lot of finger pointing, hand waving and some stern words so I sensed a bribe was coming - fortunately for us - this did not happen.