Bear Ursa

Regarding your cap, the Hyperion is notoriously bad for cap. It's ok, we understand. When you get to your anchor, make sure you turn off your MWD. When you get below 30%, broadcast for cap. When you're next to a sansha battleship activate your Nosferatu on it. And when you can afford to upgrade to a Vindicator and then to a better MWD, do that. Cap skills like capacitor management, capacitor systems operations, high speed maneuvering, and controlled bursts will help in the long run because the Vindicator isn't cap stable either, but the ship and MWD are the biggest upgrades.

Kronos is easy, 5 hammerheads for NRF and TPPH, 2 ogres for TCRC. Vargur drone bay is a little more difficult to figure out an optimal solution for. Maybe 2 ogres, 1 hammerhead, 3 hobgoblins? Drop both ogres for a TCRC, but otherwise a mishmash for NRF and TPPH?

No corp requirements. If you're planning to fly Logi you can't be under a war dec though. A lot of us have made our own corps to avoid taxes.

Depends on how bling, t2 guns/good faction abyssals are one person's bling, t2 guns and optimal faction abyssals another's, and officer guns/officer abyssals are another's. 'Good' faction abyssals in this case means near max roll on one stat, and decent positive roll on another. Including drones: Vindi w/ t2 guns, good faction abyssals, optimal skills, and implants, 2800+ Pulsemare w/ t2 guns, good faction abyssals, optimal skills and implants, 1900+ Leshak w/ t2 gun and good t2 abyssal sinks, optimal skills and implants, pre-spool 1420+ Leshak is one of the easier officer guns since it's a single gun and can be found on the market sometimes, it would bring pre-spool DPS to 1490+

I think one of the issues FCs have with TPPH rooms 1 and 2 is that because Logi are the slowest ships, anyone that has burned or should be burning to the gate is more likely to switch to long range ammo and slow down site time. Another issue I see is that while you're trying to promote it as a mark of a good Logi, drawing agro is more likely to be a mark of a bad Logi who just slams all reps into a target and then alt tabs to watch cat videos. The last issue is basically what Nicholas said, Logi should ALWAYS be trying to not draw agro. The more you practice in situations where it isn't a threat like the scenarios you mentioned, the less likely you are to draw it in areas where it is a big threat like NRF fourth wave switch or TCRC first switch.