Where to connect RX and TX on the Sainsmart UNO

The 5V pin is the output of the on-board 5V regulator. Yes, you are correct that it can be used to power external components which use a 5V connection.

The 3V3 pin is the output of the on-board 3.3V regulator. Same as above as for powering components from it.

The VIN pin is slightly more complicated. If you are not powering it from USB but rather from an external power supply, that supply is directly available on VIN. However, the ATmega328 is still powered from 5V which is available on the 5V pin after being passed through the regulator. So the VIN pin is unregulated (unless your external supply is regulated) and should probably not be used to power external components.

Unfortunately, I believe all the pins on the arduinos are only rated for 40mA. So while your power supply might be able to provide more, if you take it from the power pins you should not draw more than that.

The ethernet shield is SPI. A quick look at the schematic for the LCD shows that the pins it uses don't conflict with the SPI ethernet pins, except that pin 4 is used as the SS pin for the SD card on the ethernet shield. You have to deal with this. You might be able to cut the track on the LCD shield to pin 4 and wire it to another pin. You'd also have to change the LCD software.

The LCD shield uses analog pin 1 for the buttons, so pick other analog pins for the accelerometer.

Adafruit.com have an LCD 'backback' that allows you to drive those 16x2 displays from I2C or SPI, which reduces pin conflicts.

This is good shield resource http://shieldlist.org/ and it lists the pins for each shield.