Mi10 your simply running to many things in your head
First thing first, you already have the speakers i.e. 3 way component for front and 2 way component for rear. You also want to run the 3 way active in which case you need 3 way active xover that could be either from the HU or the amp or from a sound processor. Than you need to run your 2 way component as passive followed by the sub. All together you heading 8+1 or 2 (for sub)channel.
That's a lot. In process of getting everything right you may also want to consider make the sound too muddy with the all the speakers. There would be quite a bit of frequencies clashing in a size of an small hatchback, in your case I suppose you plan to use it in the i10 if am not wrong. With careful planning and right tuning one could avoid this. But if not done correctly it could have adverse effect on your sound stage.
Let's talk about the front stage. This would be your 3 way component in which you plan to run the midbass active and the midrange and tweeter through the passive xover. Which means you need 2 ch. for the midbass and 2 ch. to power the mids and tweeter through passive. Provided you do the modification to the passive xover as mentioned by Navin.
This also means that you would need to have TA for both the Active midbass and the passive system.
In short you would need 4 channel amp here.
Going to rear stage. This should be fine if you using it as filler balancing it with the front stage. In which case it is preferred to have this bandlimited which would be from 200hz to 3.15khz/4khz. Having too much of high freq. would pull the stage to the rear even if the gains are set at low level.
This means you need a 2 channel amp with either active xover for bandlimiting or choosing an amp that would give this possibility.
I would like to add something here, if using the rear setup without time delay could make one feel that all the sound is coming from front center but with more presence on the left side behind the driver. Having the rear set with gain set in a way where it would add little more presence is fine but without TA it would just not be that useful.
Am using the Clarion DXZ785 with front stage as 2 way passive and rear coax along with the sub with TA on all of them. I have bandlimited the rear coax with running the setup under "3 way active" and added TA to it. Have tried both with TA and without TA and can tell you, one can never enjoy the rear setup without adding TA to it. My rear acts just as fillers and after using Time alignment it adds to the center stage at the same time giving a feeling of sitting and listening to music in larger environment.
Which boils down to having 2 channel amp for rear, bandlimited and having a TA.
This leaves us with SUB section.
There is not much to do here accept for the placement of the sub and having TA on it would not make any sense.
HOW? Well in car the Sub is at the furthest listening point. Lets say you tune the system considering the driving position. In this case lets say sub is at 140cm, FR midbass is at 90cm, FR mid & tweet is at 85, FL midbass is at 130cm, FL mid & tweet is at 125cm, RL components is at 100cm and RR component is 135cm. In a given situation one would need to add time delay is such a way where by adding the difference all the speakers fall to 140cm similar to distance of the sub.
Which means one would add time delay of 50cm for the FR midbass, 55cm to FR mid & tweet, 10cm to FL midbass, 15cm to FL mid & tweet and same way to the rear setup.
That you are adding time delay to all the speakers leaving the sub so that you could have all the sound travelling in equal distance as per the driver's seat.
All this comes down to that you would need 4 active xover. where under "HIGH" setting you could use HPF of lets say around 500hz at 18db or 24db slope which means your front midrange and tweeter will be getting freq. above 500hz further getting separated by the passive xover.
Rear components can be set to "MID" setting where its getting bandlimited from 160/200hz to 3.15/4khz. or you could cross it higher as per your liking.
Front Midbass will be running active under "MIDBASS" setting as per your desire may be from HPF 60/80/100hz to 500hz LPF.
and in the end the Sub running under "SUB" setting LP under 100hz as per you desire.
In a given situation as this you need 8channel of amplification, 4 way active xoer or with TA atleast on 6channel.
The HU that you have mentioned comes with 3 way active xover. In which case you could you use MID & tweeter through passive under "high" setting, Midbass under "Mid" setting, the sub under "Sub" setting. That leaves with the rear components, which can used be if the sub amplifier is receiving signal from the HU where the HPF is at "through" and LPF is at 4khz, at which you could use LPF on the sub amplifier anything below 100hz, you could take the line output from the sub amp that is receiving the signal upto 4khz and feed it to the rear component's amplifier. since you would need to band-limit the rear components you could use HPF on it from 200hz. This way you could get band-limited output to the rear setup but you won't be able to have any TA on it.
Best I suggest is you choose a head unit that has 4 way Active xover capabilities, get Decent Two 4 channel amplifer in which case you get the desired 8 channel requirement, where you choose CH 1 & 2 for the mid&tweeter, Ch3 & CH4 for rear components and from the 2nd amplifier you choose Ch1 & Ch2 for the midbass and Ch3&Ch4 could be bridged to power the sub.
In your stated diagram you are using y connector to split signal from two channel to get 4 channel out of it, this cannot be further split by another Y cable as shown in your diagram.
The Amp I would suggest could be from Alpine MRP-F600, MBquart DSC 4125, SoundStream Reference series, Infinity amps.
MBquart DSC4125 is quite a capable amp does 125RMS x 4 and has more like a dual mono design where under bridged output gives out 500RMSx1 channel.
ANOTHER OPTION: You could also do with Clarion DXZ785 + RF3sixty.2 + Two 4 channel amps.
You could take front output from clarion feed it to RF3sixty.2 which can do 3 way active along with TA. Than use the rear output from Clarion on your rear components, this again give you the flexibility of having TA on rear, and than sub can run under SUB output.
Both these setup could push you budget by atleast 200-300$ or more depending on the choice of amplifiers you pick.