Okay well for your Radar trigger. It looks good, I question why you have it set to repeating as I believe the way it's currently set it'd just keep firing a reveal all after it gets captured a single time. which isn't really a problem either unless you have the shroud regrowing on you.
So that leaves me to believe that you simply don't have the trigger attached to the building on the map. So go to the radar you want to fire the trigger when captured and double click on it, this should bring up the Structure Options. Now in that box go to the last thing available called Attached Tag, if it says None, then there's your problem it should have the Radar Used trigger there.
Now for your firestorm trigger set...
I'm confused on a few things here...
1-Are you wanting the firestorm to fire after the ion storm begins?
2-Or are you wanting it to fire after the fighting starts?
3-Is this for a neutral house on a multiplayer map or is it suppose to end up being a trigger for the player house on a SP map?
I ask #3 because of the action you are using in it called#34 add repeating superweapon. Which would pose the problem in that all that does is give a superweapon usage ability. Thus by giving the AI (and a neutral house AI at that) a superweapon, they just don't know what to do with it. So if you're wanting this on a MP map and for it to turn on pre-existing neutral owned firestorm sections you should instead use action #92 Turn Firestorm defense online and then use the dropdown box in the parameters and set it for Neutral.
**NOTE: a few actions in that 92-94 range are not normally shown in finalsun unless you have modified your Finalsun.ini or dled the modified one. If you do not have a modified one don't worry too much. You can still set the trigger but you have to type the action # into the selection box instead of finding it in the dropdown menu. It will also not show a parameter thing but the dropdown box in the parameter value will still list the houses.**For an example you can take a look at my Perseco Terra map as it uses some firestorm walls which are activated until some stuff gets destroyed.
Now currently from what I see this is how your firestorm triggers will work out...
Map begins -> Instantly a VERY short ion storm will occur along with it Firestorm walls for the neutral house will turn on (once you change the action # that is) and a local will get set. -> The local allows the Fighting Starts trigger to go off 10 gameplay ticks later -> 2 text triggers go off and the local is cleared.
So if you want the firestorm to turn on at some point during the ionstorm then something like this needs to be made:
Trigger 1: Ion Storm
Event: Any Event (Ion storm will start at beginning of gameplay)
Action 1: Ion Storm Start -> 1000 (mainly because 10 is too short

)
Action 2: Set Local -> Firestorm Defense Online
Trigger 2: Firestorm on
Event 1: Local is Set -> Firestorm Defense Online
Event 2: Elapsed time -> 250 (these events together will cause the firestorm to turn on 1/4 the way through the ionstorm)
Action 1: #92 Turn Firestorm Defense On -> Neutral (this will turn on ALL existing, neutrally owned, firestorm walls)
Now for fighting after the firestorm you could have something as simple as this IF it is indeed an ion storm from the start of the map for 1000 ticks...
Trigger 3: Fighting Start
Event: Elapsed Time -> 1001 (note it's 1 game tick longer than how long the ion storm will last. Thus the trigger will fire 1 game tick after the ion storm ends. If you want the ion storm to start in the middle of the map you'll need something a bit more complex)
Action 1: Text trigger -> whatever your number is for the text you want
Action 2: Whatever else it is you want..
as for the 'no i'm not hiding anything' comment i made. I was making a suspicious addition to that post concerning the fact I posted on your topic right after I posted my new map thus covering up my map from being the topic shown on the forum index.