How to set up recurrent and customized auto reply in Gmail for free

TLDR, you could use our shared zap directly. 
Create / Sign up a Zapier account with your Google account, the Zapier free account could set up to 5 free zaps, which is enough for most cases.
Click button of 'Create Zap'.
For the app event, select 'Gmail'.
Select 'New Email Matching Search' for the Trigger Event.
Click 'Continue'
Sign into your Gmail account, this could be different than you Zapier account. In general, this should be the Gmail account that you want to do the auto-reply.
After sign in, your Gmail account will appear, click 'Continue' again.
In the search string, you could specify which emails you want to do the auto reply. Normally, you would like to include 'in:inbox' in the search string, otherwise even those emails you sent will trigger the zap, and cause unexpected loops.

Tip 1: you could search by label if you want to do auto replies for certain labelled emails, e.g. 'label:leads'

Tip 2: you could do recurrent email replies, if you also add a date in the search part, e.g. 'older_than:7d' for trigger to work on those email of more than 7 days old.
Click test trigger, and see if your search criteria could find out the emails that you want. Note that this will only do the search, and won't actually trigger the auto replies.
The first email found will be shown, it's a raw email display so it may look a bit overwhelming. You only need to check the email titles and date to see if they match.
Next step is to set up the action of  auto email reply. Also select 'Gmail' in the App Event part.
In the action event, select 'Reply to Email'.
Click 'Continue'
Select the account for the auto reply. In most cases, you should select the same Gmail account as the trigger setup step.
We most likely want to reply to the email found in the trigger step. In the 'Thread' box, select 'Custom', then click 'Show all options'.
Click 'Message ID', so Zapier will know which email thread to reply to.
In the 'To' text box, click 'Show all options' again.
Click 'From Email', so Zapier knows to whom the reply should be sent.
In the body, you could set up the reply context.

Tip: you could use the most fields of received email inside the template, e.g. you could put the sender name in the first line of reply, see the screen capture for more details.
Click 'Test & Continue'.
You should see an auto-replied email in the Gmail folder, if it looks fine to you, just click 'Turn on Zap'.

All future emails that matched your search string, will be auto-replied with the email template you set up.
After every thing is done, click 'Go to my Zaps' to review all the zaps.
In the Zap dashboard, you could see the newly created zap. Click context menu to rename the zap to a more meaningful one.
Type Enter key to finish renaming.
You could always disable the auto reply by turning off the zap in dashboard.
Limitation: the free Zapier account won't expire, however it could be triggered at most 100 times per month. So in this case, at most 100 auto replies could be sent every month. It's useful if you only need to do a few targeted and customized auto replies every month.