Hi The Crocster!
Welcome to Cafe Saxophone from the Skabertawe Horn Section!
;} With regard to your various points -
1. It is good to try practicing quietly as well as loudly, and if you play facing a wall you will both hear your sound more clearly and sound a little quieter. Some lounges/sitting rooms have a little too much sound absorbing material, sofas, carpets and stuff; it would be good to try and find a place to practice which is freer of such furnishings - a garage may be a good idea anyway.
2. Do you intend to have any lessons - would be really useful to set some up to make sure you get off to a good start - embouchure etc.
3. What materials are you using to learn, if any? I will certainly recommend "The Jazz Method for Tenor Saxophone" by John O'Neill - costs about £14 from Amazon, and includes CD and answers lots of basic questions. It is aimed at adult learners and should have you playing 'proper' tunes quite soon.
There are also several other books which have accompanying CDs (Tracks both with and without the Sax part. A good series to look at would be the ABRSM Jazz Grades - and maybe Grade 2 would be a useful book to get hold of - features 15 actual Jazz Tunes, albeit slightly simplified and shortened - but excellent if you want some decent tunes under your belt sooner rather than later - you could choose maybe 2 that you could learn/work on as part of your practice routine
4. Practice routines - all sorts of advice out there. Commonly this involves gradually learning certain notes - middle register first, then gradually expanding up and down - concentrating on a good sound - long notes so you get your breathing nice and steady - learning a couple of scales etc. - including learning a couple of tunes over a period of time - especially listening to the tune sufficiently before playing.
Anyway warm welcome and hope you enjoy your Tenor. Also add Charles LLoyd to your list of Tenor Sax players - brilliant latest album "Mirror" which got a 5* rating in Today's Guardian - a rare feat!
Kind regards
Tom