(Ilionej’s Twitch Affiliate anniversary: August 15th, 2017) Subscribing to Ilionej on Twitch is a good way to support the stream if you can’t live with the sole reward of her gratitude and possibly enhancing the stream content! Here are a list of perks you get for subscrib(bl)ing to Ilionej:

• Special on-stream alert
• Up to 3 exclusive sub-only emotes to use anywhere on Twitch! There are 3 tiers - prices in your currency will be shown to you by Twitch as soon as you hit the "SUBSCRIBE" button. Do not confuse these with cheer bit emotes or browser extension emotes(e.g. BTTV or FFZ).

• Use of all assigned emotes all over Discord(type !discord in chat any time to get an invitation link). You might need to sync the channel in your personal Discord settings though and some servers have the right to prohibit use of other channels’ emotes.
  
• Special role in Ilionej’s Discord server: Madie
  

• Subscriber badge beside your username in chat from 1 month to 6 years. Higher tier subscriptions will be marked by a star as seen on the right.

• Access to some special chat bot commands for as long as you stay subscribed
  
• Bypass most spam/link filters
  
• No ads during your viewing experience - hopefully
  
• Don’t have to be present to win …. uh…. once-in-a-century-giveaways..
  
• Directly support Ilionej & keep the stream running! :D
  
• Startle her with the alert when (re)subbing
  
• 1 year subscribers might receive a special gift from Ilionej. (may or may not be a Perler of the sub badge)

Yes, the streamer you subscribe to, does get a percentage revenue. Twitch Partners however receive slightly more than Twitch Affiliates. (Partnership has very high requirements, while Affiliation is a kind way of Twitch to help out smaller streamers to make some little money as well.) For details refer to the Twitch FAQ.

Via the "Subscrib(bl)e"panel on Ilionej’s Twitch page, via her subscriber page or via that “Subscribe” button you should find on her Twitch profile somewhere around the video player. Do NOT confuse it with the “Follow” button. ;) 
Other streamers may have designed their buttons and panels in other ways, but likely similar. 

Remember: Amazon Prime includes Prime Gaming (formerly Twitch Prime), which gives you one free Tier 1 subscription per month that you can use on any Twitch channel you like(if it has a subscribe button)! Streamers get the same percentage of revenue as they get for "normal" subscriptions.

Yes, gifted subscriptions are AS appreciated and have their own alerts. You can gift a sub of any of the 3 tiers and it will last a month(will not be automatically renewed). The streamer will get the same percentage of revenue as they get for "normal" subscriptions. Gift away!

Via the same button as you subscribe(you should see an option to gift subscriptions to a person or up to 100 to the community - just select your option) or by clicking on the name of the person in chat to find the button for it.

That is totally fine and actually encouraged. Just stay somewhat family friendly, reasonable and within legal measures. 

To include a message in your subscription, you must have at least been subscribed for one month(previously continuous; as of February 2019, you can have been subscribed at any point in the past, gifted or manual). This is set by Twitch. To post your message, you will need to refresh your stream and find a bar on top of your chat box that shows for how many months you have been subscribed as well as an option to show what streak(current continuous months). Click on “share”, type in your message, check your options, hit enter, TADA! There are currently no messages for gifting subscriptions to others though.

Yes, and all of Ilionej’s goals still continue throughout offline times as well as streams of other content. Ilionej always repeats offline alerts in the beginning of her next stream to spread the community love. All streams are highlighted on Twitch as well as uploaded to Youtube, so you can check if she said the truth. ;)

First check your emote menu in that server. Are Ilionej's emotes greyed out? Then most likely emotes from other servers are greyed out as well. This means, the server owner does not allow use of emotes from other servers. Unless you know the person well, there's hardly anything you can do to change that, neither can Ilionej.
If all emotes are greyed out or only Ilionej's, you might need refresh your synchronisation and wait for, say, an hour. If nothing changes, you should report the issue to Discord.