mongodb single node performance - mongodb

Question

I use MongoDB for an internal ADMIN type of application used by my team.
Mongo is installed on 1 box and no replica sets.
ADMIN application inserts 70K to 100K documents/per day and we maintain 4 months of data. DB has ~100 million documents at any given time.
When the application was deployed, it all started fine for few days. As the data kept accumulated to reach the 4 months max limit, I see severe performance issues with MongoDB.
I installed MongoDB 3.0.4 as-is on a Linux box and did not fine tune any optimization settings.
Are there any optimization settings I need to adjust?
ADMIN application has schedulers which runs every 1/2 hr to insert and purge outdated data. Given below collection with indexes defined on createdDate,env,messageId,sourceSystem, I see few queries were taking 30 min to respond.
Sample query: Count of documents with a given env,sourceSystem, but between a given range of dates. ADMIN app uses grails and the above query is created using GORM. It used to work fine in the beginning. But over the period of time, performance degraded. I tried restarting the application as well. It didn't help. I believe using the MongoDB as-is (like a Dev Mode) might be causing performance issue. Any suggestions on what to tweak in settings (perhaps cpu/mem limits etc)?
{
"_id" : ObjectId("5575e388e4b001976b5e570f"),
"createdDate" : ISODate("2015-06-07T05:00:34.040Z"),
"env" : "prod",
"messageId" : "f684b34d-a480-42a0-a7b8-69d6d18f39e5",
"payload" : "JSON or XML DATA",
"sourceSystem" : "sourceModule"
}
Update:
Indices:
[
{
"v" : 1,
"key" : {
"_id" : 1
},
"name" : "_id_",
"ns" : "admin.Message"
},
{
"v" : 1,
"key" : {
"messageId" : 1
},
"name" : "messageId_1",
"ns" : "admin.Message"
},
{
"v" : 1,
"key" : {
"createdDate" : 1
},
"name" : "createdDate_1",
"ns" : "admin.Message"
},
{
"v" : 1,
"key" : {
"sourceSystem" : 1
},
"name" : "sourceSystem_1",
"ns" : "admin.Message"
},
{
"v" : 1,
"key" : {
"env" : 1
},
"name" : "env_1",
"ns" : "admin.Message"
}
]