Is there a general rule/statement when it comes to local small logos.
Not really. You need to do some due diligence when customers ask you to print logos. For the most part, just use common sense and do some basic research to see if the logo is trademarked and if the customer has right to use it.
If a local team parent comes in to ask for a team design using the team logo is there a generic rule/form or statement that puts the responsibility on the purchaser. Is there a way to state as a designer/printer that "by you requesting the design/image I the designer assume that you have Copyright permission to duplicate and or sale the image"?
You can have the customer sign a notice or waiver. But it really won't prevent you from being accountable in an infringement lawsuit. If you reproduce existing IP without permission, you are at least partially responsible. It really depends on the specifics of the situation whether the IP owner would find fault with you, the customer or both.
Let's say you are held accountable in a lawsuit... if you can prove that you were deceived by the customer, then you may be able to sue them to recover any losses. Again, it would depend on the specifics.
Also, Teams can not hold copyright infringements on printers for using generic team names (ie: Stallions, Patriots, Chiefs, Mustangs, etc...).
Yes they can. If the team name is owned as a registered trademark, they can take action to protect it. If you are printing uniforms for sports leagues, you should ask if they have permission to use the pro sports names or logos. If they have permission through a sponsorship, you should also ask if the teams are mandated to get uniforms from official suppliers. Based on getting that info, you should be able to make an educated decision on whether you should be printing the team names.
As a general rule though, be extra careful when printing team names or logos that are intended for re-sale in a retail venue.