The short answer is yes.
Technically, your LLC is a separate entity from yourself, and so it should have its own credit history. The problem is that because your LLC is new, it has no credit history, so creditors will look at your credit history in making decisions. In fact, if they are smart, they will look at your credit history even if your LLC does have a small credit history.
Another aspect of this is that most creditors will ask someone (usually the owners) to personally guarantee the debt. This means that if the LLC can't repay the debt, the creditors can come after that person for the balance. This is done to prevent people from opening up businesses, taking out loans in the business's name, filing for bankruptcy and keeping the money. So, in this case, since you are basically a co-signer, your credit history will impact your LLC.
Yes. A supplier or the local office supply place may give you more credit than a bank, but not by much (Interest will be much higher). A starting LLC has no credit history, so yours will be the only one to consider. A partner with better credit may help.