IF your iPhone and your computer use the same Apple ID and therefore are on the same iCloud account AND if you use iCloud for photos THEN the answer to your first question is YES whatever you delete on your iPhone will be deleted on your computer and on iCloud. As far as your second question about space, please see below-
I would like you to realize and know one important thing and that is that there is NOTHING that you can do to increase the physical storage capacity of your iPhone. Your iPhone's storage capacity will forever remain the same as the day you bought it.
You have purchased ➔ iCloud Storage from Apple where you create and save your iPhone backups and synch (Not Store) your Messages, Photos, Contacts, Calendars, Notes and Reminders. Note that iCloud Storage is NOT an extension of storage capacity of your iPhone. Just wanted you to know some facts. Thanks.
Axel F.