Need some advice...

Only in parallel! And with crossover...

Or you could consider
1)remove the things in front of the JBL cone
2)Put the new tweeter coaxially ( in place of the other things) and run the wire outside ( i.e. on the grill)
3) arrange a lowpass filter for the woofer

2b)Put the tweeter aside or above the oval speaker; probably is that what you want to do: have some treble since the speakers are located in a way that the treble frequencies are not directed to your ears?!
 
It's not generally good/possible to connect speakers in series unless they're identical. Maybe you meant, in parallel.

You'll have some sort of crossover in series with the tweeter which will limit the loading of the amp to the range of frequencies above the crossover point.

You shouldn't have a problem unless you're abusive.

Clarify. Is your amp a 4ch and how are you using it (2ch or 4ch).
 
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You need to connect a capacitor in series with each tweeter to prevent the low frequencies from destroying it.

However, the tweeter and capacitor combination need to be placed in parallel with your JBL similar to what is shown in the attachement (ignore the values shown in the attachment).

A 4.7uF non-polar film capacitor may be suitable for your purposes.
 

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BTW this is a ( 1st order) series crossover for a woofer and a tweeter.
It can be done! The value of the components has to be carefully chosen
For a 2.3 Ω woofer the value of the coil will be pretty low, and the wire gauge low too ( 14 ? ). But I don't think it will work in a car environment, as the tweeter's voice coil is prone to burn easily, with just a cap for protection. Better to go 2nd order.
The woofer now works without any low pass filter, so it would benefit from some band limitation.
 

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