Using an AT&T Cell Phone In Europe

 I do not want to buy the AT&T International plan as it is very expensive (I am going for a long trip).

International day pass is *not* a purchase...

It is an add-on that you add to your phone line to cover you in case you use service. It does not charge you unless you incur charges by using data on a foreign network, making or receiving a phone call on a foreign network, or sending a text message. It is strongly advised that you add it as a safety net even if you intend to disable your phone.  Costs if you do incur charges at a pay-per-use rate are considerable. Phone calls are $3 per minute in most countries but can be as high as $5 per minute text messages are $0.50 multimedia messages are $1.30. Data rates are $2.05 per megabyte 

International day pass is capped at 10 charges per bill cycle on consumer accounts.  

I will have roaming switched off and my phone in airplane mode.

That's redundant, putting your phone in airplane mode would be sufficient

Questions:

1.  If I receive a text, do I get charged?

No. But if you're keeping your phone in airplane mode with Wi-Fi off, you would not connect to a network and would not be able to receive text messages.  With airplane mode on, Wi-Fi back on, you can receive text messages via Wi-Fi calling

2.  Is there any way to send a text without being charged?  (Use Wifi Calling)

See 1

3.  If I use Wifi calling do I get charged?

If You are calling a US number, no.

If you call a non-US number, you are subject to charges just as you would be in the United States

4.  If someone calls me does it go to voicemail?

Yes 

    If so, if I call my voicemail do I get charged?

Yes.  

5.  If I buy a local SIM,  do I still see texts people send to my phone,

No.

or do I have to constantly switch SIM's?

Yes.