Directv AM21

Sorry, they are wrong. The AM21 will not work with the HS17 genie 2.

So next question. Is there a device with a larger hdd, or am I able to replace hdd? 

Yes you can add a larger external Esata hard drive that replaces the internal one or a company called weaknees.com can replace the internal drive with a larger one and even copy the existing programs.

AM21 discontinued years ago so not supported by the Genie-2 (HS17). The new Local Channel Connector (LCC), that is still technically in testing (for a ridiculously long time) only supports the 2nd and 3rd generation Genie (HR44 and HR54).

You can use an external eSATA HDD like prior models. As it is used instead of the internal, it must be larger than 2TB to be worth it.

Do NOT use a 3rd party to try and replace the internal as that is a violation of service. You don't own the box and it is against the Terms of Service to modify the internal hardware. DirecTV would be well in their right to charge you if you messed with the innards of the box.

weaknees is an authorized DTV retailer so they are allowed to service DTV receivers and even TiVo receivers.

Granted if you go with weaknees to replace the internal drive you will have to deal with weaknees to repair it if and when or lose the internal drive if you cancel and return it or there is a need to return it to DTV.

Yet DirecTV's service has been design specifically against transferring for recordings as they are encrypted to their exact drive/DVR pairing. Authorized retailers are resellers of lease equipment, but should not have permission to take apart the boxes as those go back to DirecTV for authorized techs to work on them.

Not saying it isn't impossible for OP to get this done, but I heavily caution on this as they accept all consequences if they go that route.

They can only transfer programs to the same DVR.