The printed rules leave room for interpretation so your DM must rule it
You can use your action to create a pact weapon in your empty hand. You can choose the form that this melee weapon takes each time you create it (...) This weapon counts as magical for the purpose of overcoming resistance and immunity to damage. (PHB 107)
You can transform one magic weapon into your pact weapon by performing a special ritual while you hold the weapon. (...) You can then dismiss the weapon, shunting it to an extradimensional space, and it appears whenever you create your pact weapon thereafter. (PHB 108)
What the rules don't say is whether the transformed magic weapon holds its form or can also take a form chosen by the Warlock, and I can read the rules-as-written both ways.
The first paragraph refers to an otherwise nonexistent weapon, which can be shaped, whereas the second refers to an existent weapon which should keep its form, hence "it appears", "it" the weapon.
The first paragraph describes what happens to any weapon, nonexistent or existent which the Warlock summons, hence "it appears whenever you create", and "create" assumes "you can choose the form".
I don't think you can apply "specific beats general" here as there is no necessary contradiction between the specific and general rule.
I suppose the main idea of the second part of the rule is to allow you to have magical weapons that do extra cool stuff, and sometimes that might be tied to the specific form (for example, a Trident of Fish Command). But in any case, as is (for some frustratingly, for others liberatingly) frequent in D&D 5e your DM needs to rule this one.
Official ruling
If your table puts stock in official rulings, then the answer to this question is "you cannot change the form" (as pointed out in @DerekStucki's answer):
Once the bond is formed, the magic weapon appears whenever you call your pact weapon to you, and the intent is that you can’t change the magic weapon’s form when it appears. For example, if you bond with a flame tongue (longsword) and send the weapon to the feature’s extradimensional space, the weapon comes back as a longsword when you summon it. You don’t get to turn it into a club. Similarly, if you bond with a dagger of venom, you can’t summon it as a maul; it’s always a dagger. (Sage Advice Compendium, v1.14, p. 5)
Yup
Both require attunement, but you've got three attunement "slots" so there's no problem there.
One requires the wielder be a Warlock, the other just requires the wielder be a spellcaster. So no problems there.
Looking elsewhere, the only conflict we might run into would be "Multiple Items of the Same Kind" (DMG p.141). But that's directed at things—like layering two pair of gloves or boots—that would be physically incompatible. Holding two one-handed objects really doesn't seem to run afoul of it.
If this seems overpowered, just remember what it's "costing" the warlock: two of her three attuned items, along with whatever it took to get two very rare magic items, plus a free hand for material components. And it only benefits her spells which require attack rolls. It's a lot, but it's not worse than a rogue who got her hands on a +3 longbow and a Manual of Quickness of Action. The point is: if your game's got very rare magic in enough quantity for a single character to grab two harmonizing items, that's going to be a lot of power.
Best Answer
RAW, no
The Rod is an arcane focus, not a weapon. It could be used as an improvised weapon, but it is still not a weapon.
Rules as fun
It sure seems similar to a club or quarterstaff to me. A DM certainly could choose to accept it as a +1 version of either of those weapons.