Did the citizens or merchants of Roman Empire go travel to Southeast Asia for trading with these countries?

The best source on this is a text called the Periplus of the Erythraean Sea, which is a merchant's handbook written by someone from Roman-era Egypt. It describes the routes and ports one goes to sailing down the Red Sea and into the Indian Ocean, both across to India itself and down the coast of Africa. The Periplus only describes destinations as far as the western shore of India; its author doesn't seem to have ventured or know anything farther east than that. We don't have any positive evidence of Romans trading directly with southeast Asia, but it's not impossible that someone could have made the trip. The bulk of the trade further east, though, would have been carried by Indians or people from the region itself, and they were probably the ones who carried Roman coins there.

One fascinating detail of the Periplus; it reports a port on the east coast of Africa as the source of cinnamon. Cinnamon was not grown in Africa in ancient times, it was from Indonesia; but islanders had learned the navigational feat of sailing straight across the Indian Ocean to Africa to trade, so the Roman merchant, finding cinnamon there, thought that was where it came from.

There was a regular trading route, from what is now the Persian Gulf across the Indian ocean to India and back, using the trade winds which ran opposite directions at different times of the year.

Certainly hundreds, if not thousands of boats sailed this route during the Roman period.

Overland there were regular Roman forts in the Sinai peninsular and what is today Saudi Arabia and Yemen.

The Romans had a substantial and lucrative sea trade with South Asia trading at ports along the coastline as far as what is now Kolkatta. These routes were called the Spice and Incense Routes. So there is every chance that they sailed further into South East Asia.

People no, goods and coins were moved across the Silk Road - silk appears in Rome and Roman coins appear in the silk production nation.

At the same time Egyptian/Roman/Greek traders were travelling/trading with Western India, internal trade carried goods to Eastern India where they went into the Monsoon moderated trade between India and China.

there was a famous route called the silk road thousands of years old before Rome or Greece traders would travers this perilous journey to trade goods silk was highly prized among the elite hence the name silk road Romans loved silk there is your answer the perilous silk road was the reason for the opening of the world by explorers trying to find another better way to these treasures

No, there is no evidence that Romans themselves went that far. The coins traveled there via middlemen, and the goods they paid for traveled back to Rome the same way.

Roman glass products from around the age of Augustus Caesar (first century CE) have been found in tombs of that era in Korea, too.