May I have a question about Lax airport please?

If I go Eva airline I have to check in at Eva air counter, and if I go China airline I have to check in at China air counter. Is that correct? And by the time I check in, all my baggages will be drop at the counter in the same time, is that correct? When I stop at Taipei airport, do I need to go to security check my passport one more time or I just need to go straight and find the next Gate Terminal number and wait for the next Fly. Sorry because I have never been flying out of US for long times, i came to US with my parents since I was 9 years, First time flying back to VN alone and little bit scare.

Yes, you must check in at the counter of the airline you are flying, that airline will take your baggage, At Taipei you will be directed to where ever you need to go, if you are connecting and do not exit security you do not go through passport control (immigration). If you exit, yes you will need to go back through immigration. No need to be scared, airports are well marked and there are tons of people who can direct you so ask.

When you get off the plane at Taipei just look at the information screens for the number of the gate where your next flight will depart from, and GO there. If you need to go through any security or anything, you will find it on the way and it will be impossible to miss it.

If you fly EVA, you will go to the EVA ticket counter to check-in. If you go China Airlines, you will go to the China Airlines' ticket counter to check-in. Both ticket counters are at the Tom Bradley International Terminal. When you check-in, you will drop off any bags to be checked in. Anything that is really important such as medication should be kept with you and brought onto the aircraft in a smaller luggage. When you check-in, you will also receive your boarding pass.

At Taipei when you connect, you should not have to go through security again and will just head to the next gate. Taipei or Taiwan Taoyuan International Airport is pretty easy to get around. I have been there a few times. Gates are pretty clearly marked. You can also look at the in-flight magazine to check out the gate locations.

Enjoy your trip. Both EVA and China Airlines offer excellent service. No need to worry about your connection. If you are worried, talk to a flight attendant before landing and they can guide you.

1.) If I go Eva airline I have to check in at Eva air counter, and if I go China airline I have to check in at China air counter. Is that correct?

Correct.

2.) And by the time I check in, all my baggages will be drop at the counter in the same time, is that correct?

Correct.

3.) When I stop at Taipei airport, do I need to go to security check my passport one more time or I just need to go straight and find the next Gate Terminal number and wait for the next Fly.

Unlikely for the passport check with Customs since Taipei is only a transfer point. However, if Tawain follows the US Rules of airport security you may be going through security screening again. (Ask a security officer for assistance if you need it.)

Enjoy your trip to Vietnam. (I dream of the foods. )