One thing that often arises is the idea that the 40k games should be more deadly.
The other thing receiving much hate is the vindicare dodging everything.

I have one idea that can do both. Or at least make fights potentielly last longer while nefing the vindicare.

That idea is incorporating an increasing check penalty to characteristic checks thats resets at the start of the round.
So you get a cummulative penalty of -10 to ckecks after the first time you checked on that characteristic each round.

The following HR is best used with the BC rules for lightning attack and such.

Example:
A Vindicare is being shot at by 5 guys, all of them are lucky and succeed at their to hit roll.
When the assassin dodged the first he has his full dodge of say 100.
At the second dodge he gets his first -10 penalty and dodges at 90% chance.
The third attack is dodged at 90% chance and so on, with the fifth and last attack "only" has 60% left.

If that Vindicare tried to use stealth later that turn (however he'd manage to come later than those 5 guys) he'd do so at -50% penalty, because it is again agility he'd be using.
For shooting one of the attackers he'd not get a penalty, because he's not used BS yet.

Example 2:
A Khornite champion is in melee with 3 guardsmen. One of them gets to go before the Khornite, hitting him with his combatknife.
If the Champion decides to parry that blow he will have a -10 penalty on his attack because both, melee attack and parry use the BS characteristic.
Should he instead dodge he could attack at full potential.

I assume you'd put some sort of loophole in there for people with Swift/Lightning Attack. Even so, I don't really fancy it. There are already ganging up bonuses that cover the situation with the berserker (I know it was just an example). This multi-action problem really only occurs for a very limited set of characters. If you're trying to fix vindicares, I think that's an issue that should be addressed separately. Perhaps don't allow heavier than X armor, or limit dodges in a turn.

In our current game you must declare a dodge before the attack roll is made. When you do so you must move 1 meter in any direction except for toward the shooter (this mandatory movement isn't mandatory if you are behind cover). If you are in melee combat when this occurs you can choose not to dodge or to move and take the hit from your opponent (note: you can't dodge or parry the attack from your melee opponent that you are "fleeing" from). Shooters into melee still take -20 and can hit their teammates.

This just blew my mind. Since we just started using BC rules for multiple attacks, dodging is going to me much less effective for the vindicare assassin in close combat against a single opponent. Degrees of success matter. It's not like we ever had a problem with it in the first place, it just something that hasn't come up yet while playing. He normally avoids close combat like the plague.

My issue with your proposed system is that it penalises lower level characters more so than it helps limit the high level ones that are the problem.

A house rule i've always run with is that any roll of 01-05 is a critical pass and any roll of 96-100 is a critical fail. If degrees of success matter you can consider it the maximum that character could have rolled against their current stat (ie for a critical pass it would be stat - 1, for a critical fail 100 - stat). As the system is percentile (01 to 100) it shouldn't be possible to have a situation where all your modifiers add up to over 100 and you auto-pass without rolling - the only situation when you shouldn't be rolling is if there is no chance of failure or there aren't multiple levels of success possible.

Another thing to limit dodges getting over the top is to remember that you must be aware of the attack or effect to be able to dodge it. The text on the vindicare may well say that they can dodge things not normally dodgeable (like titan stomp attacks) however a silenced sniper rifle firing from over a kilometre away and the vindicare can't see the muzzle flash - no dodge!

Keep these two simple rules in mind and the system stops getting bogged down quite so much with broken combinations