Not really sure what you are asking for in #1. Are you asking if a PTR record is used in a mail server setup? Technically no it is not, but as a PTR record is used as the counterpoint for an A record, there are merits to having it properly configured (also, depending on other servers configurations regarding doing lookups to authenticate your server, it can affect mail flow if not properly configured).
Let's take a step back.
Mail is routed to you based on MX records that point your domain to the appropriate FQDN. This FQDN then has an A record configured for it so that you can translate its name to an IP address. A PTR record allows you to do a lookup based on the IP address to make sure that what is returned is the FQDN that in turn has an A record pointing to the same IP. This is why it is also referred to as a circle check as one gets you to the other one and vice versa.
Now keep in mind that mail flow in to your domain does not equal mail flow out of your domain. Small organization may have the same ingress/egress path, but many organizations do not, so looking at an MX record will show you where inbound email is sent, this is not necessarily where outbound email comes from.
I am sure there are automated tools to check for records, but I would recommend becoming familiar with either nslookup (Windows) or dig (Linux), or both, to do your lookups manually. This will let you query against the DNS servers your system normally does, as well as allowing you to manually do lookups against other DNS servers (so you can verify results both internally and externally).
Are you looking to resolve a specific issue, verify a specific configuration, or just educating yourself on how the various DNS records are used?