Attempting to convert my .htaccess file to NGINX notation.

I have browse the online help guides but am still battling.

Would anybody mind helping. My .htaccess is:

Options -Indexes
Options +FollowSymLinks  

# Enable ETag
FileETag none                       

# Set expiration header
ExpiresActive on
ExpiresDefault A2592000
Header append Cache-Control "public"

# Compress some text file types
AddOutputFilterByType DEFLATE text/html text/plain text/css text/xml application/x-javascript text/javascript application/javascript application/json

# Deactivate compression for buggy browsers
BrowserMatch ^Mozilla/4 gzip-only-text/html
BrowserMatch ^Mozilla/4\.0[678] no-gzip
BrowserMatch \bMSIE !no-gzip !gzip-only-text/html

# Set header information for proxies
Header append Vary User-Agent

########################################################
# Rewrite Rules
########################################################

RewriteEngine on

# Require SSL (HTTPS) on the signup page
RewriteCond %{SERVER_PORT} 80 
RewriteCond %{REQUEST_URI} ^/signup/?
RewriteRule ^(.*)$ https://www.example.com/$1 [R,L]

# Redirect /signup/plan or /signup/plan/ ->  /signup/index.php?account_type=plan
RewriteRule ^signup/([A-Za-z]+)/?$ /signup/index.php?account_type=$1 [NC,L]

# Redirect /home/123 or /home/123/ ->  home.php?home_id=123
RewriteRule ^home/([0-9]+)/?$ home.php?home_id=$1 [NC,L]

# Redirect /homes/ in case someone made a typo when it should have been /home/
RewriteRule ^homes/([0-9]+)/?$ home.php?home_id=$1 [NC,L] 

###########################################################
# Error Handling
###########################################################

#ErrorDocument 400 /
#ErrorDocument 401 /
#ErrorDocument 403 /
#ErrorDocument 404 /
#ErrorDocument 500 /


#################################################
# Default Settings
#################################################

# hide apache server signaute on apache generated pages (e.g. 404)
ServerSignature Off 

UPDATE:

For that GZIP compression, this seems to operate. However I still haven't determined how you can my my HTTP Rewrites rules yet.

 gzip             on;
  gzip_min_length  1000;
  gzip_proxied     expired no-cache no-store private auth;
  gzip_types       text/plain application/xml;
  gzip_disable     "MSIE [1-6]\.";

UPDATE 2

I attempted changing my htaccess rewrite rules using the following NGINX rules but this does not seem to work. Any ideas what I am doing wrong?

# Redirect /signup/planname or /signup/planname/ ->  /signup/index.php?account_type=planname
rewrite  ^signup/([A-Za-z]+)/?$ /signup/index.php?account_type=$1  last;

# Redirect /home/123 or /home/123/ ->  home.php?home_id=123
rewrite  ^home/([0-9]+)/?$ home.php?home_id=$1  last;

# Redirect /homes/ in case someone made a typo when it should have been /home/
rewrite  ^homes/([0-9]+)/?$ home.php?home_id=$1  last;

UPDATE 3

Per your comments ought to below, Now i possess the following NGINX config but am still getting problems

# gzip
gzip             on;
gzip_min_length  1000;
gzip_proxied     expired no-cache no-store private auth;
gzip_types       text/plain application/xml;
gzip_disable     "MSIE [1-6]\.";


# Require SSL (HTTPS) on the signup page
# ====== THIS DOESN'T WORK AND BREAKS NGINX
# I obviously change "example.com" to be my actual domain
if (location /signup/) {
   rewrite ^ https://www.example.com$request_uri? permanent;
}


# Redirect /signup/planname or /signup/planname/ ->  /signup/index.php?account_type=planname
rewrite  ^signup/([A-Za-z] +)/?$ /signup/index.php?account_type=$1  last;

# Redirect /home/123 or /home/123/ ->  home.php?home_id=123
# Also, Redirect /homes/ in case someone made a typo when it should have been /home/
rewrite  ^/homes?/([0-9]+)/?$  /home.php?home_id=$1?  last;

When I see in documentation, your rules (not conds) ought to be like this:

A:

 RewriteCond %{SERVER_PORT} 80 
 RewriteCond %{REQUEST_URI} ^/signup/?
 RewriteRule ^(.*)$ https://www.example.com/$1

N (see here for more information) :

if (location /signup) {
   rewrite ^ https://pma.clinicacgm.0$request_uri? permanent;
}

A:

RewriteRule ^home/([0-9]+)/?$ home.php?home_id=$1
RewriteRule ^homes/([0-9]+)/?$ home.php?home_id=$1

N:

 rewrite  ^/homes?/([0-9]+)/?$  /home.php?home_id=$1?  last;