Hi.
There are some chances to handle your requirements using 'spaCy' library (Python 3.6). It recognizes part of speech - for example: for your first sentence it throws:
Jack PROPN nsubj
needs VERB ROOT
to PART aux
provide VERB xcomp
details NOUN dobj
of ADP prep
his ADJ poss
age NOUN pobj
, PUNCT punct
salary NOUN conj
and CCONJ cc
education NOUN conj
so the subject is already retrieved. The 'provide' verb is xcomp (not root) what means it is a predicative or clausal complement without its own subject. Words 'age', 'salary' and 'education' are conjuncts or objects of preposition, so they may be considered as objects like in your table.
For other sentences the situation changes and there's a need to implement some demanding behavior of the parser. For example: in 2nd sentence the verb associated is a root one. I have no idea how to retrieve these values - it can be tricky and for sure needs to be developed in some smart way. I don't understand why in 5. the associated verb is null not 'select' for application form. What constraints should be set to learn a script to recognize that?
Anyway, further study is required. If you need my help send a message. I guess, this should be hourly paid if extend beyond the budget.
Cheers, Peter.